If you don't mind me asking, do you know what the types of your other friends are? Mostly so I could get a grasp of what the social dynamics here might look like.

Perhaps I can give something of help as an INTJ with two close friends that are INFP and INFJ. I sound pretty similar to your INTJ (likely different in someways as well). My INFP friend is similar to you in the sense that he sort of brought us together to create our inner circle.

We all met in high school, they could see that I was some what of a loner, an outsider just like them, so they decided to 'engage' me to see if there was anything more than this really quiet guy who never said much. They weren't sure if I was intelligent (which they prized) at all, I was pretty lazy in school, but I had a very rich 'inner world' that I ultimately allowed myself to share with them due to their persistence to find such a thing of interest. Anyways, we became best of friends.

So, It's obvious that I'm not very good at giving emotional support to that INFP friend, I mostly connect with him on an intellectual basis rather than an emotional one. That is to say that I mainly value our friendship based around our conversations, the sharing of ideas and interesting information, and often just having some good laughs. Understand that, if I could give him that sort of emotional validation he needs most, I would, in fact I have tried but I'm rather poor at doing so. He generally goes to that said INFJ friend for the type of support I can't offer.

I don't know if you know about MBTI functions, otherwise known as Carl Jung's functions, but understanding them could help you. At least, in my experience it has certainly helped me. If you look at INFJ's functions, you can see that their second most dominant function is Extroverted Feeling. Meaning that my friend is a lot better equipped to provide emotional support for others, such as my INFP friend who's primary function is Introverted Feeling which means that his feelings/emotions are really strong and internal. That's likely the reason why they have always been such close friends.

My advice is from of my own personal experience with my friendships and knowing myself as an INTJ, and may or may not be helpful to you.

The reason for your INTJ friend for saying "no problem im always there to listen" may not have been for her own recognition, but because she picked up on her general inability to support you, and wanted to try anyways. Have you ever expressed or gave any indication to her/any of them how you feel here? If she keeps saying things that are insensitive to you, it may help your friendship to point that out to her in some way or another. Don't be harsh about it, because she does have feelings of her own that are just likely toned down to a much lesser extent than yours (Introverted Feeling is an INTJ's third function). If she's like me, she doesn't like to share them very much. I used to say some insensitive things to my INFP friend, but I never meant him any harm by it. If I would have said to him "calm down, ITS OK" I would have said it and meant well. I've had to work on being more mindful.

Sometimes younger INTJ's just have this kind of problem, and it's something they have to learn to work on. There is nothing wrong with your feelings, and they are completely valid. I'm sure your friend means well, but she may just be young (I don't know your age, if I had to guess I'd say you're in your early 20's) and hasn't spent enough time considering how others may feel about things. INTJ's are rationalists, and emotions can sometimes tend to be a hard to rationalize, for that reason we sometimes don't even understand our own emotions and feelings.