You should read the most recent post by SGB- it's good advice and says what a lot of us are advising.
You are right that CBT is not about avoiding triggers- but at the same time, you are also having counselling for your issues. Who is telling you to carry on dating- the CBT person or the counsellor?
Whichever, it's not really their place to advise to that degree. If you have said to them that you feel like carrying on dating, I can see them saying 'ok we will work on that if you like'- but I doubt they are actively suggesting you date. (I know a lot of counsellors as friends and colleagues, and have some knowledge of CBT via my own work.)
I don't think you can see it as others can. It's not 'normal' behaviour to get chatting to a strange guy in a bar and within a few minutes tell him you are on a date and where you met that date. Your date was justified in being a bit narked that you disappeared and then showed up talking to someone else. His behaviour was OTT, BTW, and he's an arse- but many decent men would have made a mental note of your behaviour and seen it was a red flag. A nicer man may have ended the evening soon-ish but more politely.
It is also not 'normal' behaviour to come onto a forum and talk so much about what- with hindsight- should be just a bad date where you made a tit of yourself. It would not warrant calling the Samaritans - it might warrant a call to a friend and a bit of a laugh over it and the awareness you'd made yourself vulnerable to something that could have ended much worse- rape, violence etc.
It's no good defending your readiness to date by comparing it with behaviour at work; work is a controlled, structured and professional environment with clear boundaries. Dating is about your emotions and you have to set your own boundaries.
If I was a bloke I'd not want to date you. You have too much 'stuff' going on psychologically. You'd be hard work, fragile, a loose cannon. You might even spend hours writing about me in a journal and post it on a public forum!!!!
Why not just broaden your circle of friends- meet men and women- join a group like MeetUp which is in all big cities- and stop looking for a relationship for a while. You aren't ready - too much 'stuff' going on in your head that needs sorting.