While I was sleeping he made 2 BTC transactions in that binance and successfully withdraw them via P2P to his bank account. After that he asked me for a refund because his own binance account was fixed.
You did logged in to the account after selling it to see activities. You should not.
2 hours ago I entered binance again, and which tells me that he has taken it out of my device and I had to re-enter and ask for a code, for me it is a very suspicious reason that he is entering the account with the aim of stealing the funds
My argument is that I can't make a refund as he already used an account (who knows for that he used it???). His arguments - 0. Once I offered him (the 4th time) to change details of the account on yours he refused.
No, you can't but you need to prove it that he used the account. He must deposited the 2 BTC. Give a screenshot of the deposit with blockchain tx ID. And also give some screenshot of the P2P trade.
If someone was depositing 2 BTC, then I have no idea for only $70 why would they care.