(dropping in mid thread here, hopefully I'll be clear where I'm talking directly to the OP and where I'm quoting other people in the conversation)
I was in a similar-but-not-identical position to you some years ago (around your age actually, I'm 36 now and things are going fine) so can relate to the feeling. I think most people feel this way at points in their lives.
> you're a worthy human being and don't need to seek approval
This is a significant point. First make sure you like yourself; from there social confidence does not come from believing other people will like you and want to hang around with you, social confidence comes form knowing you'll be perfectly fine if they don't.
Don't take that as "it is their loss" or "I'm better off without them" because those are negative trains of thought which will make you seem (and feel) arrogant, instead try use the frame of mind "well, that didn't work out, shame, but fine, lets try something else". The more relaxed attitude to things not working out as desired will reduce any air of desperation you might be giving off which will help you be more comfortable to be around.
> > I also feel resistance when I ask someone to go out on outings
There could be many reasons for this. People have limited time, especially those with GF's/wives and families. Adding new people to their social circle may just seem like something they don't have time for right now, and if that is the case it isn't a slight against you personally.
It may also be that what you are suggesting just isn't their thing. Have you tried finding like minded people outside your current family and work circles? If you have hobbies then finding a local club relating to one of them is a good way to meet people with whom you more naturally have something to talk about.
> Insecure men also struggle with their manliness.
I didn't read a specific "manliness" issue here, but rather a more general "socially awkward" one. The rest of that paragraph are on point though: there are many in the same boat, many in far worse situations because they fell into something less than ideal, and finding the right people simple isn't predictable. I say "right people" not "right person" there as I don't believe there is one right person for anyone - there are a number of people you could love, a number of people who could love you, and there will be more people in the compatibility cross-over of that venn diagram than you might fear.
> > I still don't have GF or wife
I suggest not worrying overly about that, if you try too hard to make it happen you'll look desperate and either scare people off or attract the wrong sort who are out to take advantage. I've been single for a little over a decade now (initially burned by a long term relationship that went sour so I locked myself away a bit, more recently just because the right situations haven't occurred (or when they have it hasn't worked out)) and it really isn't a problem. Concentrate on finding friends, if something else happens after that then that is a bonus. Heck, once you develop close friends they might introduce you to people they know who that might work for you with.
If you are specifically worried about that and feel it is something that is missing form your life you could try things like speed dating, I know a couple of people that has worked out well for. Everyone in the room knows they are in a similar position in the respect and the event is regimented which removes some of the awkwardness of approaching each other, and the worst that can happen is that you've lost a couple of hours of an evening and it might help you to go and realise the range of people who do turn up including people who you might otherwise assume could just walk into a bar and pull on command.
> > What is wrong with me, seriously ?
Almost certainly nothing more than is wrong with the rest of us!