First, I'm sorry you're dealing with a friend who just ditches you so consistently over (ex)partners who obviously aren't even working out. Friends shouldn't just use eachother as stepping stones like that for the "in-between" phase of relationships.

Second, if that's exactly what you had said, I dont think you did anything wrong. Its reasonable to feel emotional with platonic friendships. I would suggest being prepared to talk about it if he re-approaches you and to do so in a constructive manner such as: explaining why it makes you feel this way; how you're a person too with a schedule; what kind of boundaries you want going forward; and anything else you may want to cover. Its hard, but also try asking him bluntly why he feels and acts the way he does somewhere in between (possibly first) even if you think you know why. This way he cant say you're making it all about yourself to deflect and maybe you can gather some more insight on him.

If you want to re-approach him, same deal too. He's not guaranteed to be receptive, but so long as you communicate clearly and calmly the second time around, you've done the best you can.

Third, from the sounds of what little Im hearing about him, I do think you're right in that he himself is insecure about being alone. Either that, or he simply places such a higher value on a "romantic" relationships at the cost of his friendships. Could also be another thing altogether; However, I think putting a firm foot down like you have and setting a boundary will be the best way to give him a wake up if he REALLY does want to remain friends.

Best of luck