I posted this on the PS4 section, but I guess it can help lot of other-platforms people, so I cross-post here as well (hope this is allowed)
You may have noticed that animal pens are big, really big, and hard to place, for their size mainly.
But there is something that probably not everybody (especially new players) have noticed and that will make the struggle to find a suitable location even more consistent, if not impossible.
While you summon your pen in placing mode, by default, and for some weird reason, the pen is placed very deep into the ground, this will prevent the structure to be placed almost everywhere.
If you are wondering what is wrong when you try to place the pen in a large open space and the system keeps giving you a big fat red cross, good chances are is for this reason.
( and yes, once you get this little problem fixed, they can be easily placed on natural ground as well )
So, from the starting position when it spawns in build mode, you will have to rise it ( cycling the build mode until you find the decrease/increase height option ) of 3 or 4 steps at least.
This will put the pen in a more normal depth compared to the ground (any ground/foundations) and make it WAY more easy to be placed. Play with it until you find the right depth for the building.
Hope this little tip helps, and that the default position will be changed to a more friendly-one for non-expert players.