With the older stories in the Bible, especially the short ones, it is real easy to focus on the wrong things.
Why was Er killed? The author didn't want you to focus on it - he slaps an quick "he did evil," on it because he needs to establish that Tamar is not barren, but also not have a heir to the property. So if the author didn't think it was important to record the why, you should avoid focusing on it. Focus on the lesson.
The hero is Tamar. This is a story about how men treat women terribly, especially when sex is involved.
Ancient Israelite culture was all screwed up about women. They couldn't testify, they couldn't own property. They couldn't consent to sex without being purchased. If they didn't belong to a man, they had to beg for survival. (Compared to today's world where women can work, but they earn 25 percent less, and they can testify, but it isn't trusted fully. And they can control their bodies, sometimes, but men fight about it, without inviting women to the conversation, and they surely don't want to pay for it.)
Enter Onan, who is supposed to give her a heir, so she can be dependant on someone who loves her, and we'll hopefully outlive her. And this duty us a burden to Onan. If she does not conceive, Onan gets 2/3 of his father's property. Is she does, he hats 1/4. So the jerk has sex with her, repeatedly, without concern for her. (Is this like rape?) But Tamar is in no position to change it, or stop his repeated "attempts." Fortunately, today's culture has come so far that men no longer use women for sex without being responsible for the consequences, and always care for the female's needs.
So Tamar gets shuffled off to her father's house, where she will be a burden to men who don't want her, and may die before her, leaving her destitute. Eventually, Tamar intentionally hatches a plan to get her back to a more stable place. It is a clever ruse involving prostitution, and exposing hypocrisy, and it works. Again, fortunately, today we have come so far. Male use of pornography is ubiquitous, but 50 Shades of Grey is shocking. Men are still praised for having many partners, while women are shamed.
So Er died, because if he lived, this story would be boring.