Did I do the right thing?

I’ve been struggling with this all day. I had to fire one of my techs today. I’m 99% sure I did the right thing, but feel awful about it. Here’s the quick version of what went down. He was Help Desk admin, so he had some admin-level credentials and access to a fair few systems with risk and trust involved. One day, last week, he had a user reach out to him after-hours, needing admin credentialed approval for a software update on their laptop. Now, either out of sheer laziness, lapse in all judgment, or a weird crush he had on this user, he decided that rather than remote into the user’s laptop, type his creds in to get the update pushed through, and call it a day… he simply gave the employee his admin-level username and password over a Teams chat message. To say this enraged me when I discovered it is an understatement. I took this guy under my wing and gave him trust that has been hard to come by. I look at the IT infrastructure at our organization as a baby of mine. I had a major hand in building it from the ground up and any threat to it, I take as a personal affront. But I’ve spent 100s of hours with this guy training him, building him up, showing him proper procedures and imparting useful IT knowledge and experience on him. We became somewhat close, and I feel bad throwing him out on his ass so abruptly. But at the end of the day, how could I ever trust him again? Does anyone feel like I overreacted? Am I just being hard on myself?