Neurotypicals seem to never realize that playing along when someone initiates an interaction with you is orders of magnitude easier than initiating an interaction. And it's not just because of the typical reasons like "fear of rejection" or "fear of embarrassment".
You have no social life and you want to get invited places. Someone invites you somewhere. That's easy (well, in comparison, because it may still be difficult for other reasons). All you have to do then is just play along.
But if you're initiating the interactions, there are many more calculations that have to be done. You have to figure out what to say to them. You have to figure out in what situations it's okay to approach them. You have to figure out how to read signs of interest. You have to figure out how often to approach them, because too little is disinterested and too much is clingy. And even if you do everything right, you probably still won't be invited anywhere because they may like you enough to interact with you if they happen to be near you but not enough to invite you anywhere.
And when you try to open up about struggling to socialize, you're met with "that's not true, you got invited to this one place this one time, you're just being negative".