I haven't heard a good reason why Puerto Rico should not be a state.
It has over 3 million US citizens
It's far closer to the mainland than either Alaska or Hawai'i
It has more people than at least 18 current states
It's bigger than both Delaware and Rhode Island
It's been a US territory far longer (>120 years) than most current states that were not part of the original 13. Hawai'i was a territory for less than 60 years before achieving statehood.
Because they don't want to be?
I haven't researched this issue myself, but my DH has and we've had some discussions on the topic, so forgive me if some of my information is out of date or misunderstood.
My understanding is that for PR to become a state, they would have to make some changes to their constitution to meet the requirements for a state constitution. These changes are controversial among the PR population. There may be other reasons that some PR citizens vote against statehood. As previously mentioned, PR has voted numerous times on the issue of statehood, and the referendums (referendi?) have mostly failed or passed by very narrow margins. Certainly nowhere near 2/3 majority. Many blame this on poor wording, which the current iteration avoids, but it still passed by a very narrow margin, indicating that a large portion of the population doesn't want statehood.
Just to be clear, I do actually support statehood for both PR and DC if they can get it. But it is by no means a simple question, and there are certainly arguments against.
"It's not normal" is not one of those arguments. Even if we discount the original 13 states, every other existing state at one time was not a state and applied for statehood using an established process. To say that no more territories are allowed to follow that process because "it's tradition now" is nonsense.