Why is the Paste context menu not coming up in iPad and iPhone in my web page?

I built a responsive site where I can't paste text in textboxes or textareas when on iPhone or iPad, either Safari or Chrome wdo the same. It's hard to explain, but basically, you can hold down your finger on some text and the Copy menu would show up, you touch it and the text is copied. But when you go to a textbox or textarea and try to paste the text there, it just doesn't show the Paste menu.

Since this is so hard to explain, please see this small video I made showing the problem: https://youtu.be/yq6Nobd-Fuc

Everything works fine on Android phones.

Anyone has ever experienced this issue?