OP definitely should have checked what the fee was before making that withdrawal. Binance didn't do anything wrong at all; the fee is what it is, and it's the customer's responsibility to know it beforehand.
It's not worth it to withdraw small amounts of bitcoin from exchanges right now, and I'm fairly certain it's because they all use high fees in order to get the bitcoin into their customers' wallets as fast as possible (which you have to pay for, of course). I've noticed on Kucoin that withdrawal fees change as the network becomes more/less congested, but they're usually never cheap when it comes to bitcoin. The days of being able to get bitcoin out of your account for, say, 10k sats are over--at least for now.