Your neighbor was way out of line, especially since he is a psychologist. He should know better than to offer insights and critiques that were not asked for. If he wanted to deepen your friendship, he could have offered to share a pattern in your relationship with him that the two of you could work on. But his angry and emotional accusations would never accomplish that goal.
I realize this is complicated because the wives are friends. I hope it’s reasonable for you to take some distance from this man. You can always plead that you are too busy to do things as a foursome and encourage your wife to continue to see her friend. I see no reason for you to subject yourself to more comments from the husband.
I think you did listen, in spite of the tone and manner in which your neighbor talked to you. Your letter indicates you’ve thought about what he said and that you own that you have some personal work to do. In your 60s, you are still interested in growing and improving. Give yourself enormous credit for that.
As for bridging the gap? I don’t know if you can. If your neighbor needs to be “right” and “superior”, he isn’t going to accept that you are working on yourself as best you can. I suppose you could tell him — again — that you do think about his words and that you are working on improving. But do also tell him that you want to be his friend, not his client, and insist that he stop offering advice. Then change the subject to some interest you share. If he won’t stop analyzing you, then do take that step back.
I wish you well,