A big mistake? I don't think so. A big mistake is thinking that something is definitely going to ha=ppen. Actually, many people lose big money exactly because of such way of thinking. They bet $1,000 on a team that, according to the majority of bettors, should win the game, being absolutely confident that after the game they will be $100 richer(1.1x multiplier), and lose $1,000 because of bad luck. Haven't you read such stories on this very forum? I've read tons of them.
If the vast majority were always right, anyone with $1,000 could stop working and start living off sports betting alone. But the reality is that you are very likely to lose at least one bet within 10 bets with 1.1x payout, and thus your overall profit will be slightly negative.
Correct. And the house-edge is always there. If 10 people will bet $1,000 each at 1.1 and no one bet on the opposing team, there is a high tendency that the 11th bettor onwards won't be receiving a 1.1 odds. The odds will change from 1.1 to 1.09 or even lower.