Why can't you transfer Pokemon in Pokemon GO?

If you are trying to transfer and you cannot, it might just be a bug in the game, or you are using an older phone that can't handle the game very well.

In general, the game does allow you to transfer Pokemon, but only to the Professor.

To do so, first tap to view the Pokemon that you want to transfer. Then, from that screen, tap on the circle in the lower right that looks like three lines. Once you do that, you will see an option to transfer that Pokemon to the Professor. If you click it, it will warn you that you can't get your Pokemon back if you complete the transfer.

If you do transfer your Pokemon, you will receive one candy of whatever type the Pokemon is, in order to help others power up or evolve.

They may add trading to the game in the future, but for now, that is the only way to move a Pokemon out of your inventory.