Good landlords provide decent quality accommodation, charge a fair rent, and deal with problems promptly once they are made aware of them. That includes problems with the property, and problems caused by the tenant.
Bad landlords fall down on one or more of the above.
You’re not a bad landlord, or a bad person, because someone who passed all the letting criteria turned out to be antisocial. But it IS up to you to deal with it appropriately.
Also perhaps have a word with your agency and find out what sort of references the tenant provided from a previous landlord. You might want to tighten up on process, e.g. ask to see them yourself in future and be more involved in the process of choosing future tenants.
We were once talked (by the agent) into accepting a tenant who was in a new relationship and had failed the credit check - they offered to pay a year’s rent up front. We accepted. At the end of the year, they paid one month’s rent, and that was it. By the time we got them out they had cost us £6K in unpaid rent, £1,500 in legal and court fees, and it cost £4,000 to put right the mess they had made of the property. At least we got to keep the deposit.
After that, we resolved to never again accept a tenant who didn’t pass all the checks and have immaculate references.