I think its a fair comment on the film's light touch around why sub-prime lending boomed in the years prior to 2007. Your question asks what was happening in 2002 or 2005; I think the key thing about the pre-crisis years is that there was a complex system generating mortgage debt that matured throughout the period up to 2007 and afterwards. Focussing specifically on why 2007 became the tipping point is perhaps to use too much hindsight. In my view it is probably more helpful to think of an unstable complex system that tended towards a crisis; even in the film there is a scene in which Michael Burry says something along the lines of "I wasn't wrong, I was just early". What can be usefully addressed is the question as to what was happening in the US economy in years leading up to 2007 that created this unstable system. There is obviously a huge amount of economic and historical literature around the crisis. Most of my understanding has come from two sources: Niall Fergusson The Great Degeneration (2013) and Adam Tooze Crashed (2018). The below is an attempt to summarise my understanding, which is heavily derivative of these two books:
First it is worth emphasising the incentive structure faced by banking executives: As with most large corporations today, the executives of the large US and global banks in the pre-crisis era were heavily incentivised to maximise shareholder value (stock awards/options make up the majority of executive pay). One of the easiest ways to do this is to increase the bank's leverage (purchase more assets against a relatively small equity base). The key point about the years leading up to the crisis was that the financial regulation in place expressly permitted the banks to do just that; the Basel regulations at this time specified the amount of equity a bank was required to hold compared to assets on a risk-weighted basis (if an asset was considered low- or no-risk the banks could stuff their balance sheets with as much as they could get without having to hold any more equity against it). And the risk weightings for these assets were provided initially by the banks themselves and then by the ratings agencies...who were paid by the banks and competed with each other for banking business (hugely incentivised to underplay the riskiness of any security with which the banks presented them).
So why were mortgage backed securities and their associated derivatives the assets of choice for banks to feed through this perverse incentive structure? There were a number of forces distorting the US mortgage market that made investing in mortgages an attractive prospect for banks. Government Sponsored Enterprises (Freddie Mac, Fannie Mae) acted as a back-stop to the mortgage market; they were licensed to purchase mortgages meeting certain quality criteria, using the extremely cheap debt that they had access to given their high credit rating as GSEs. This essentially begat the originate-to-distribute mortgage system, whereby a commercial bank could originate a mortgage loan and then immediately turn around and sell it to the GSE, which in turn enables them to go an make more loans. This had been going on in the US in one form or another since the 30s but the pace and risk of lending was increased in the 90s as the US government issued targets for mortgage lending to low-income areas. It was viewed as politically desirable to increase the number of US citizens that owned their own homes, but the unintended (or perhaps intended??) consequence was an increase in sub-prime lending.
At the same time financial innovators were coming up with evermore creative ways to "manage" this increasing risk inherent in mortgage lending. A common principle in finance is that risk can be diversified away; if two risky assets have uncorrelated returns and are combined into a single portfolio, the risk of the portfolio is less than the risk of either of the individual assets (when one is down the other might be up). As any explanation of the myriad complexities of CDOs, CDSs, CDOs squared etc is far beyond my knowledge, I will make the sweeping statement that pretty much all of these financial products were predicated on the principle that risk could be reduced through diversification: buying one dodgy mortgage may be risky, but buying small pieces of hundreds or even thousands is fine. What are the chances they will all go bad at the same time right? And this is where the unsuitability of the risk analysis of banks and the ratings agencies came into play. They were viewing the return one mortgage as being fundamentally unrelated to the return on another mortgage. This was incorrect because underlying economic forces could hit all mortgages at the same time; there simply wasn't a precedent for this in the relatively small data sets on which they were building their "Value at Risk" models.
Finally there were two additional market distorting factors that were affecting the broader US economy, which allowed this unsustainable lending to go on without a correction for much longer than it should have under 'normal' circumstances.
Firstly, the federal reserve took a very one-sided approach to monetary policy. It would intervene by cutting interest rates if asset prices dropped too rapidly but would not intervene to increase rates if prices rose too rapidly, providing the rise did not affect the Fed's measure of inflation, which curiously included consumer price indices but excluded house price indices. This meant that the cheap credit could keep flowing into the housing market despite the rapid house price appreciation of the pre-crisis years (which in turn encourages speculative investments related to house prices: find some way to borrow at cheap rates, invest in a rising housing market and sell out before anyone realises the houses have appreciated far beyond anything close to fundamental value).
Secondly, China contributed in a big way to the persistently low interest rates of the pre-crisis period. After joining the WTO in 2001 China managed to build up a massive current account surplus against the US (huge imports of Chinese goods into the US), which in turn led to huge capital flows from China into the US (US pays for Chinese goods in dollars, which the Chinese in turn invest in dollar denominated securities). The majority of this capital would have flown into US government debt, thereby keeping interest rates much lower than they would have been for much longer than they would have stayed.
So to summarise: leading up to 2007 you have an economy that is flooded with cheap credit through a combination of one-sided monetary policy and huge flows of Chinese capital into US debt, meaning the banks have got plenty of capital just looking for a home (pun not intended). The banks in turn are incentivised by corporate remuneration norms and financial regulation to absorb as much of this cheap credit as they can and plough it into productive assets, and due to the government drive to get the US population on the housing ladder, the asset of choice was sub-prime mortgages. Financial innovation just exacerbated the whole thing by creating nifty ways to pretend that risk had just disappeared due to fundamentally misunderstanding return correlations.
I appreciate the thrust of your question was why 2007 but I am not sure it is possible to answer that with any conviction; there is no generally accepted science behind predicting when the heady waves of economic exuberance will turn into fear, but certainly it seems likely that if some of the afore mentioned factors were different the market correction could have occurred earlier or later. I hope that is useful.