Pretty much Catra and Hordak are the same person, two abused people who continue to work for the regime that abused them in the first place and both work their ass off in trying to prove to their Family that they are worth something, but Hordak found someone who validated him and told him he was beautiful the way he was AND he was willing to walk across to the other side with them.
Remember, Hordak was actually thinking about slowing the portal work, just to stay with Entrapta longer, after she told him "What's the rush? We could keep working on it until it's perfect." Entrapta wanted him to stay longer and he was willing to do that. The guy who spent decades working on building the Fright Zone and a portal, was ready to slow down production, just to stay with his lab partner longer.
Hell, Entrapta probably was right in the fact that Hordak would understand that opening the portal would cause reality to break. Hordak would listen to her suggestion and not even open the portal.
But Catra, who could have been happy in the Crimson Wastes with Scorpia, just had to one up Adora one last time and just had to spite her. She was still wanting to let Adora lose one last time. She had a chance to let everything go and become her own person, and she just fucking couldn't do it. Her inability to let go of the past caused everyone around her to suffer.
Then, Catra electrocuted Entrapta when she told her no, sent her to Hell Island and then lied to Hordak about her betraying him. The guy who has such low self-esteem that he'll easily believe someone would betray him because he views himself as a failure and is worthless.