Other mistake: When Luke is reunited with R2D2 aboard the Millennium Falcon, R2 plays the original hologram of Princess Leia from A New Hope. It is being displayed on the floor, to Luke's right. He tells R2-D2 that was a cheap move, and R2-D2 turns his head to look at Luke. Problem is, the device that he is using to project the image is on the part of his head that turns. We see the beam of light move when R2 moves his head, but when Luke turns his attention back to the hologram, it is still in the same place.
Continuity mistake: When Leia and Rey feel Luke's force fading, Rey has a dark, burned, non-bleeding wound on her right arm. After Kylo enters the abandoned mine, he sees Rey through the force. The wound from before is now bright red as if it were still fresh and bleeding.
Continuity mistake: When Rey meets Luke for the first time, the sun changes between shots.
Continuity mistake: While Rey is practising with the pole and the lightsaber, the sun changes between shots.
Answer: As he says, "let the past die. Kill it, if you have to." Han was his past - he didn't hate his father, but his existence was holding Kylo Ren back from reaching his full potential, or so he believes. The principle is demonstrated earlier in the movie when he can't bring himself to kill Leia, but has no issue with the other TIE pilots blasting the bridge and (he thinks) killing her. He wants to free himself from the shackles of his parents, who cause him such internal conflict. Remove the source of the conflict and he believes he can move on to greater things. Of course, arguably his position is a bit naive, and his actions will actually cause him greater problems down the line.