TL; DR: Different circumstances, different political positions of the inhabitants. Also, race.

First, some background. The expansion of the United States has for the most part been at the whims of political and business interests, as the US sought economic, military, or arguably imperial gains to compete with other major world powers. There’s a group of contentious Supreme Court cases known as the “Insular Cases” in the early 1900s that established that the US has control over overseas territories; these cases were largely about business interests. Keep in mind that these cases, as well as some acts of Congress since then, have defined what we call the US’ territories.

Alaska, Hawaii, and Puerto Rico were each acquired under unique circumstances. Alaska was purchased from Russia, who didn’t want to keep sinking money into it and hoped that making it a US territory would put America into competition with one of Russia’s geopolitical rivals, the United Kingdom. In 1958, over 80% of its population voted in favor of statehood. Hawaii was ruled by an indigenous kingdom until 1893, when it was overthrown by a group consisting largely of American missionaries and businessmen. They established a temporary Republic of Hawaii with the end goal of joining the US (they called themselves “the Annexation Club” behind closed doors). In 1898, during the Spanish-American War, Hawaii was annexed as a territory. In 1959, with 93% of the population voting in favor, it became a state.

That brings us to Puerto Rico. In the early 1890s, there had been theorizing in American government circles about establishing bases & naval stations in the Caribbean; Puerto Rico was one of the islands considered for purchase or annexation for that purpose. During the Spanish-American War, the US invaded and occupied the Spanish territories of Puerto Rico and Cuba. Spain ceded both to the US at the end of the war, with Puerto Rico becoming a territory and Cuba became an independent protectorate.

This is where the circumstances of Alaska, Hawaii, and Puerto Rico diverge. Puerto Rico had two major factors that set it apart from the other two territories: a vibrant independence movement, and the race of its inhabitants. Both Alaska and Hawaii were largely occupied by white Americans, who either were American or explicitly wanted to be. Puerto Rico, even prior to the American takeover in 1898, had a vibrant independence movement. After the takeover, Puerto Rico consistently had an independence-oriented political party, which at one time voted for independence from the US (1914) and led an armed uprising (1950). Part of that uprising included an assassination attempt on President Harry Truman. Those political parties don’t exist as a significant organization anymore, but there’s still an undercurrent in the population of Puerto Rico who want independence.

We also should talk about race. Puerto Ricans were considered a separate race of people by many in the US, and this affected how they as a territory were viewed. This is most well-known through the case of an American doctor named Cornelius Rhoads, who went to Puerto Rico in 1932 as part of a public health project. In letters to friends, he referred to Puerto Rican patients as “experimental animals”, also writing that “the matter of consideration for the patients’ welfare plays no role here”. Below is an excerpt from a letter he wrote in 1931:

“[Puerto Ricans] are beyond doubt the dirtiest, laziest, most degenerate and thievish race of men ever inhabiting this sphere … They are even lower than Italians. What the island needs is not public health work but a tidal wave or something to totally exterminate the population. It might then be livable. I have done my best to further the process of extermination by killing off 8 and transplanting cancer into several more. The latter has not resulted in any fatalities so far.”

This letter was found by a member of his staff, who feared for his safety, resigned, and sent the letter to the president of the Puerto Rican Nationalist Part, who published it. This caused a scandal on the island, but not on the mainland, where Rhoads was widely recognized for his work in public health.

So, while Alaska and Hawaii were actively seeking statehood, elements of the Puerto Rican population wanted independence, in part because of their unequal racial treatment. That’s an undercurrent that never entirely went away – some ugly comparisons were made during the federal government’s response (or lack thereof) to Hurricanes Irma and Maria in 2017.

However, during the 20th century Puerto Rico also got significantly closer to the US economically, using the dollar and importing/exporting mostly to and from the US. This appears to have moderated the push for independence, especially recently. Over the last ten years, Puerto Rico has held three different referendums on the topic of statehood. There is an active portion of the population that wants statehood, cracking 50% in 2020, but it’s barely a majority. Which brings us back to politics, where the US Congress has not considered Puerto Rico for statehood due to the perceived political consequences of two more senators, a couple more representatives, and having to redo the stars on the flag.

If you’re interested in the topic of US territories, I’d recommend starting with How to Hide an Empire by historian Daniel Immerwahr – it’s a good, if biased introduction to the history of the US outside the 50 states.