New giveaways

you are probably trying to giveaway games that were available free previously, these games got removed from the giveaway list and therefore you cannot find them.

You may bought games that are not allowed to be given away because e.g. they were free some time ago :P

If you are unable to find some titles in the drop down menu for giveaways when Steam still has them for sale, they have almost certainly been removed after they were free on other sites.

What they said. ^^

thanks