I am in betting from a very short time - I just placed my first bet

I have this very dumb question.
My understanding of bets is like this (please correct me if I am wrong):
an odd of 6 means that the backer is betting 1 and the layer 5.
an odd of 11 means that the backer is betting 1 to win 10 from the layer.
The expected behavior from the above will be that the backer will try to get a bigger odd while the layer will try to place a bet at a smaller odd.
But I see on betangel and betfair that the situation is exactly the opposite - the backers are trying to bet at smaller odds while the layers at bigger odds.
Can somebody explain what is going on?
Cheers!