Coin exchange markets create the coin "out of thin air "
You first buy the 0.0001 BTC from Binance or any local coin exchange markets.
You give 3.5 dolar to Binance and Binance add 0.0001 btc to your account.
In this transaction, really, Binance gives you BTC ?

Firstly, not your keys not your bitcoin. Having said that, no coin is not created out of thin air, they do need to have enough bitcoin in reserve to cover all the positions of their clients or else they would risk going bankrupt in the even of having a significant amount of withdrawals at the same time and that is something that may happen. I guess they could opt for taking some risk, just like real banks do, a create some bitcoin without having reserves, but I think that is a very risky move and that it could potentially be detected which would carry a loss of confidence and massive withdrawals at the worst possible moment.