"(...) increasing the retirement age (...) possibly takes jobs from
young people and stifles their career."
Since this is often surfaces as "the conventional wisdom" (not necessarily in economics circles), let's present a simple argument, that shows that there are bound to be distinct effects for people already in the labor force, compared to the people that have not yet started their working period in life.
To bring in the surface the core effect, assume a constant population, and a constant demand for workers (that does not mean necessarily constant output of course, since productivity and efficiency may rise).
Assume that in this society, people start working as they enter their 21st year, and retire when the enter their 61th year (40 years of work). An old person should retire today -but he doesn't: he will stay on for another year (say, because the government raised the mandatory retirement age).
Then, the young person that was about to enter the labor force in order to replace him, will have to stay out of it for one more year. He will now enter the labor force when entering his 22nd year and he will exit when he will enter his 62nd year. But this means that this person will work again for 40 years: Raising the retirement age, does not mean raising the numbers of years worked for the new/future workers. What happens is that their working life shifts as regards its beginning and end on their personal age-time, but not as regards its lifetime duration.
Does this "stifle their careers"? One could reasonably argue that starting one year later gives you one more year to accumulate human capital through education and training -and so when you enter the labor force, you will enter it better prepared than if the change in retirement age had not happened.
Casually observing western societies, this is what appears to be happening: people tend to acquire more and more education, and so also start working later in life. At the individual (or mass media) level, this may be negatively experienced/pictured as "high unemployment for young people" and "difficulty to get a job that makes the young people accumulating more education in their attempt to find a job". I presented above an alternative perspective on the matter.
But as regards those that were already workers when the change happened, and so have entered on the labor force in the beginning of their 21st year, will now work in total 41 years. If we envision a gradual rise in professional ranks and income, the change in retirement age will mean that they may have to stay one more year "where they were", and in that sense, increasing the retirement age may appear to "stifle their careers". But there is also Arrow's "Learning by doing": human capital increase due to on-the-job experience (a verified phenomenon even in a perfectly static environments). So this one more year will not be a total waste in terms of increases in income earning capacity -and it may pay off more for the younger workers, than for the older ones (since the former will gain it earlier in their working life). So the "career-stifling" argument gets a little weaker, even for the class of workers-already.
Obviously this is a very abstract approach to the matter... for example, what happens to societies where population is rising? How many people can a society afford to invest in -create human capital for young non-workers- at any given time?
...but I believe it reveals one aspect of the matter that we tend to overlook.