Girl's Behavior

Should friends with benefits hold hands when out?

So, I've been with this girl for 3 years, the last year on and off and then 1 years no contact, and this year we've been fuck friends basically, we agreed and promised eachother not to go together back again, sometimes we go eat out or do some activities as friends and i would like to hold hands but she refuses and cannot a give a reasonable explanation why not, it seems it's just an innocent thing friends do when out, it makes the girl feel safe and the man is reassured that nobody will try to hurt his girl friend, i made it clear that it was really important for me to have an explanation of the reason she doesn't want to do it, She also sometimes acts weird when we're around other people and avoids having too much body contact with me.
She isn't a very popular girl around man, very NOT confident about herself and how her body looks, i have definitely made her much more confident then she was with compliments in the time we were together, so know I'm trippin' and i have a theory... I always knew she struggled to find someone else, although she keeps saying that she doesn't wanna find another relationship because she got hurt from the last one i know she just can't find a man to like her in a special way like it was with me, maybe because she's getting older maybe she's just unlucky, but my theory is that she doesn't wants other men to see us together and think thta we are a couple so that she at least has more chances to find a man that likes her, and having me around is basically a signal to men that she's available, if we were to hold hands they would think she's not.. that's hurtful because although i care about her I don't like being used.
Should friends with benefits hold hands when out?
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