Why can't I absorb a dragon soul?

Do you also have the Unofficial Dragonborn Patch installed (separate from the Unofficial Skyrim Patch)?

If not, install it. One of its fixes is:

Dragonborn's changes to DragonActorScript.psc have now been properly merged with the fixes done in the USKP. Dragon soul absorbtion is now working 100% correctly.

According to the Unofficial Dragonborn Patch's mod description, the load order should be like this:

Skyrim.esm
Update.esm
Unofficial Skyrim Patch.esp
Dawnguard.esm
Unofficial Dawnguard Patch.esp
Hearthfires.esm
Unofficial Hearthfire Patch.esp
Dragonborn.esm
Unofficial Dragonborn Patch.esp
HighResTexturePack01.esp
HighResTexturePack02.esp
HighResTexturePack03.esp
Unofficial High Resolution Patch.esp

Also as a reply to this answer, you shouldn't load Dragonborn after USKP, as it could undo the fixes of USKP. If unsure, just let LOOT take care of the load order.

Install the other Unofficial Patches if you have their DLCs too: Dawnguard, Hearthfire, High Resolution DLC.

Also, see the troubleshooting steps for the 'cannot absorb dragon souls' issue listed at the Unofficial Dragonborn Patch Nexus forums sticky post by Arthmoor, one of the UDGP developers:

Check for: dragonactorscript.pex and/or mqkilldragonscript.pex. Remove them if present. They are from dragon mods that came as loose files.

DSAMG - Dragon Soul Absorb More Glorious, and Diversified Dragons are known to cause this. Those mods need to be updated with a Dragonborn patch that incorporates the fixes from the UDBP.

Skyrim Unbound will cause this as well due to the script being unaware of the changes for Dragonborn.

Others may be a factor as well.

Note too that the offending mod may have the script packaged inside a BSA. That will need to be handled by that mod's author.

If you are using Mod Organizer and are here to report issues with dragon souls, sorry, but you're on your own as we do not support issues caused by incorrectly letting that program modify the BSA load order system the game has. Your post is likely to just be ignored. We don't have time to keep fending off false bug reports caused by people who insist on unpacking their BSA files using the program and thus subverting the entire system the game relies on for proper behavior.

It seems that there is a conflict between the unofficial skyrim patch and the dragonborn expansion.

After I placed dragonborn after the USKP in the load order I could absorb dragon souls again.