Is there any reason that this would be impossible?

The feat has no prerequisites and other characters can take it.

What combination of conditions make this feat disappear from the list?

Is that character in a campaign with content sharing on, or does the player of the Paladin own that Feat? Because Dual Wielder is from the PHB and NOT a free accessible feat.

There is content sharing and it is my campaign and I'm the DM so I can change things and add it to other characters.

I checked that the other chars can take it, I even turned prerequisites off just to see if it was it but no.

Quote from Hazilon >>

There is content sharing and it is my campaign and I'm the DM so I can change things and add it to other characters.

I checked that the other chars can take it, I even turned prerequisites off just to see if it was it but no.

 The only explanation I can think of is that the Paladin already has that feat, as a variant human or something.