How to let someone know they are avoidant?

He's actually pretty reasonable when it comes to criticism, if told in a gentle way by someone he trusts. A week after we broke up, I met up with him and had a talk with him about him being emotionally distant. Back then I didn't know about the different attachment types, so it was the best information I could provide him with at the time. I was hesitant to tell him back then too, in fear he wouldn't take it well. In reality, he ended up hearing me out about it all, and he even acknowledged that some of the things I mentioned could be true. When I asked if he wanted me to send him some links to do some research on his own on it, he said "yeah, sure". I thought he understood, and asked if he would give us another try. He looked sad and shooked his head.

As for why I decided to try harder to make it work was because I felt like I hadn't been patient enough. I see myself as secure with a hint of anxious from my past. This meant I was secure at the start of our relationship, but then went through a difficult time with things outside of our relationship and also got influenced by outsiders, which pulled me a bit back to my anxious past. Before this, I had thought his behaviour was new to me (never experienced an avoidant person), but that I should give him the time and space he needs. Suddenly, others around me told me his behaviour wasn't okay and that I should push him into being more emotionally intimate. Sadly, I listened to this instead of my own reasoning.

I don't really have any insecurities when it comes to relationships aside from my own mistakes. Let's be real, everyone makes mistakes. Some people choose to ignore them, and some choose to reflect on them. I am the latter. I don't fear being alone, and I definitely don't cling on to others because I think they are my only choice. Rather, I stick to them (if they want me in their lives) because every person in my life is unique and can't be replaced, and I care about them. Sometimes, I cut people out of my life if I see it as necessary. I don't mind being only friends with my ex though, I just need some time to truly accept that it's over. I just want him to be able to be happy at some point, even if it's with someone else. In order for this to happen though, he needs to realise he's avoidant and that he can work on it.

He wouldn't try to win me back. I've asked him if he's sure of his decision, and he said yes without any hesitation. Honestly, I don't even think there's any chance we'd ever be together again. So the two outcomes would be 1. He does some research and decides that maybe he should consider this for his next relationship, or 2. He will react negatively and distance further. As things are at the moment, further distance would mean him cutting all contact. Our current interactions are already minimal. Once a week (or less), I send him a message about trivial stuff. He usually shuts them down by replying in a way that makes it hard for me to keep the conversation going and seems disinterested. Despite this, he still claims he wants me as a friend. 

But yeah, you might just be right. Maybe I should just leave him alone about this.

Avoidant attachment impacts an individual's ability to have a healthy intimate relationship, true.

But, the main motivator for an avoidant to heal deep wounds inflicted when they were children, is often NOT A desire to be in a relationship.

I don't know any DA, personally, that sought healing initially so they could be better at intimacy.

Not that it doesn't happen.

The DA i know sought healing when they hurt enough internally to want to begin to understand themselves and the struggles they have.

It may or may not have to do with a romantic relationship.
It might have to do with their relationship with their families, their children, the world, themselves.

Anxious attachment are more likely, i presume, to be motivated to figure out how to have a relationship.

And, it's may be that he is capable of more intimacy with a different partner. It's hard to say, as his ex partner, because you contributed to any dynamic that existed.

So, as an avoidant, i see clear signs he isn't interested in your input on this, and I would agree that it isn't your place to offer him advice for the success of his future relationships.

I do notice that AP's here often tend to point to the severity of their ex partners issues while minimizing their own. Maybe their self assessment is accurate, maybe not. But a lot of AP partners are only "slightly anxious" or "situationally anxious" or "secure but i took bad advice" or somehow healthier than the partners they are on the internet posting about. I don't assume that this assessment is correct, and i don't assume it isn't.

I'm just trying to provide a different perspective.

I wish you the very best, however you choose to proceed with your own processes!

As tempting as it is, it is not your job to educate him, he will come to his own conclusions and will seek his own truth, when the time comes. I am myself tempted to reach out to my DA and tell him about all this, but it's none of my business, where he gets his emotional health and healing from. Look, if it is working for him just as the way things are, who am I to change that and who am I to decide, what works for him. That is his cross to bear. 

it's absolutely not true across the board- i do see it quite a bit from new posters, inquiring about their partner or ex partner tho. I see a lot of "mildly anxious" posters posting about "deeply avoidant" partners and i just kind of suspect that the balance is a little more equal, based in the content of the posts.

It's hard to say of course, but repeated attempts to influence an ex partner by educating them about their dysfunction (being met with resistance) and then making internet inquiries seeking further advice about how to educate an ex partner about their dysfunction (who isn't interested or openly receptive), seems like pretty preoccupied and codependent behavior to me.

i think it can be difficult to recognize or accept one's own level of dysfunction without honest feedback, which i think is helpful and readily available on this forum.

Well I'll pipe up. For reasons other than wanting to get them back, I directed my lovely little "ex avoidant" to this forum. I just told them it gave me a better understanding of myself.
If you don't necessarily want to win them back, how much harm can it do?
What are they going to do, dump you even more. ;-P