Another reason is you're shy,and if you're female and middle aged,more than likely you were raised by a Mom who drilled the "women shall be quiet and stay in the background" bit into you as a very young girl. I know mine did-using my astrological sign as an excuse. (I'm a Leo & she was fearful I'd become a ham) While I've gotten better at getting rid of the old programming,there are times when it comes back-usually it involves when someone requests to hear me play...esp live. The old "mom tape" combines with suddenly doubting myself and my abilities on the instrument,no matter what I'm playing. (guitar,mandolin & uke are may main instruments)
Another one is "I don't sing". (I use this even tho in another life,I was an alto in a choir) Well you don't have to sing-you can play instrumentals or just fingerpick chord progressions. Of my main three instruments,I find the uke is the one that makes people smile immediately. They just want to hear you,and it's usually without judgement.
So-how to go past the "I'll only play at home syndrome?" For those who live in houses with a porch,weather permitting,go out and sit on the porch and play. You still have the comfort of home and more than likely people will just keep walking down the street. If you live in a complex,go to the pool area or anywhere you can just sit outside.If nothing else,hang out near the laundry room and play. (I say this assuming you live in a very safe complex with nice neighbors-use common sense here!) Other choices would include public parks,beaches,by the lake,etc. Always use common sense and I never recommend going to any outdoor public area by yourself.
I do recommend you join a local ukulele club,if one is nearby, If not,you could form your own! There's nothing like having ukulele buddies for friendship & support. Music us a gift & it's meant to be shared!