I like to be a few minutes early to everything, I find it less stressful. But I can see the value in seeing what it is like if you do run late. It doesn't ruin relationships or result in beng fired or other horrible things unless you are usually late.

It seems like your t is giving you a chance to be late and have that not be a disaster. It seems like it would be a good thing for you to experience, if your being early is driven by perfectionism. Better to work thru it in therapy before you do actually end up somewhere late. Being late at some point in your life is pretty much guaranteed.