You have to get and keep the bead of the side you are putting on the rim off of the beadseat and in the spoke channel. The side that is already on needs to be pushed out of the spoke channel. Otherwise there won't be room for it, the tube and the side you are trying to put on.
Some new tires you might have to leave alone after you've gotten them as far as you can go with them. So go have a pint or cup'a. When finished, see if you can get a few more millimeters over the rim. Then go while away your time with something else again. Then rinse and repeat.
Though it's been a long time since I've ever had issues. Since realizing that I needed to push the bead seat of the side that is already on the rim completely out of the spoke channel and onto it's bead seat, then I've had few issues with tires.
Now if you can't get the first side of the tire on the rim, then are you really certain both are 27.5 tires. What's the ISO size say? Hopefully both are something x 584. And hopefully the rim is 584 BSD too.