I am having a sub-site to which there are 2 groups with full control, one is the default Owners group and another is custom group added by me, both groups have Full Control permission, but Why does this happen that only when user is in Site Owners group he can share the site with other users while the same user when in custom group with full control, cannot share the site with other users. I tried finding the reason but no luck can someone point out it to me
If you go to site settings > site permissions in sharepoint 2013. You can change the default in Access Request settings in order to let members share this site. Refer the below image
It seems that only default group's members can share site with other users. An Article that I found claims that it may be because of some extra permissions granted behind the scenes to default groups.
You can make a group default by going to the group > setting > Set as Default Group. Hope this helps.