Suppose there are two options: (1) take a gamble with 50% chance you win \$100 and 50% chance you lose \$110 or (2) don't take the gamble at all and win/lose nothing. Would the risk-neutral take the gamble or not?
The definition of a risk-neutral individual is someone who is indifferent between a guaranteed amount and the expected outcome of the gamble, which is -\$5 in this case. But since \$0 is only guaranteed amount does that mean all individuals who would take the gamble are risk-seekers, since \$0 is greater than the expected payoff?