I tend to get possessive at the sight of someone touching what's mine

It depends what they are touching and how they are treating it.
My two most treasured possessions are an MP3 player my kids bought me and my noise cancelling headphones.
I would let someone else use them but only someone I knew and who would take care of them.

If theyre being disrespectful then you're completely in the right to feel that way. Maybe youre worried they'll damage it

your mistake is thinking you own something

No, it's normal.

Not really

Lack of money

You need to open up and accept others.

I am guessing that in early childhood You had peers, maybe at daycare, a sibling, cousin, or even another child in your neighborhood during playdates at home or the park/playground, took toys away from You that You were playing with, other children are selfish and want what they don't have and take them away one way or another. I have a strong feeling that this happened to You, which strengthened your sense of possessions, You don't like others taking what is yours.