Hi, I’d like to share some insight from an INFJ female’s point of view, if you do not mind.
For an INTJ male to introduce you to his parents, I would think he had some interest. Some possibilities: (i) he needs some time to himself, after something “monumental” and/or emotional (to him), or (ii) his parents may have made some observations. I do think it may have been the former.
My INTJ used to converse with me over text on a near-daily basis. He would even apologise when he responded a day later. However; as we got to know each other better, I accepted that his “silences” were just him taking time out for himself, be it at home or a respite from work. I have an INFP close female friend who shared with me that these periods of silence are her being on “hermit” mode.
I hope this helps.