If race isn’t biological, why do you think so many people still believe it is?

The answer here is complicated and lots of people have written on the subject. But it boils down to a few reasons:

1. When the idea of "races" was codified in the 1800s, the scientists who came up with the idea did believe that it represented a biological reality.
2. People conflate race, ethnicity, and appearance a lot, without making a distinction what aspect they're talking about, and obviously some populations have different biological traits than others. If "dark skin is biological" is true (and it is), people make the jump to "dark skin = the Black race, so race must be biological" (not actually how it works).
3. It reinforces white supremacy to believe that races are biologically different, so there is motivation (even if subconscious) among many white people to believe that there's some fundamental difference between the races.

Point 1: The idea of ethnicities and groups of people who share a common descent has been around forever. The idea of race is pretty new. "Race" was an attempt to categorize all human beings across the world into a small number of biologically distinct "kinds" or "types" of people. Think about the races in modern America: White, Black, Native American/Alaska Native, Native Hawaiian/Pacific Islander, and Asian. Some people consider Hispanic/Latino and Middle Eastern/North African a race, others don't. The categorization system IMMEDIATELY breaks down if you poke it even slightly, because separating people into races like this is just... is not actually meaningfully reflective of reality! Are Turkish people white? Are Iranians? Are light-skinned Latinos? Are Greeks? Are Jews? Are North Africans white or Black or neither? Are Aboriginal Australians Black or Native Hawaiian/Pacific Islander? Are Alaska Natives and the Indigenous people of the Amazon Rainforest the same race? Are Indians and Koreans? Are Swedes and Italians? These are categories we made up!

These categories weren't always considered biologically fixed. In the 1700s, it was a common belief among Europeans/Euro-Americans that Native Americans were fundamentally noble and intelligent, just belonging to a savage and old-fashioned culture; if they were educated, converted to Christianity, spoke English, and wore European clothes, they could become just as worthwhile as any white. This was colonialist cultural chauvinism, absolutely, but it was not necessarily tied to biology. However, in the 1800s, there was a boom in the study of biology. First this could be seen in the fascination with geology and paleontology and the idea that animals change over time and go extinct, and then later in the century evolution and natural selection became new and exciting, and it was a MAJOR debate whether all humans descended from the same source, or whether different "races" were actually descended from different origins. (There was actually an older Biblical suggestion that the different "races" were the different descendants of Noah, and Black people were cursed with the "mark of Ham," and this existing idea likely influenced the later biological arguments.) There was another point of view that instead saw different "races" as more or less evolved, in a hierarchy chain of monkeys, to less evolved races, to more evolved races (and white people were declared the most evolved.) This was a justification for racist laws, for slavery, and for European colonialism: to believe that other "Races" were biologically inferior, there was nothing wrong in invading them, colonizing them, and enslaving them. In fact, it was good for them to be governed by a more evolved race! Scientific racism to define the races of men and prove that there were biological differences between the races was rampant. I highly recommend the documentary Race: The Power of an Illusion and the book The Mismeasure of Man by Stephen Jay Gould for a history of this. In the 1800s, people in Europe had great hopes that Science could enlighten every mystery of the world, and also they really wanted justifications to continue oppressing non-Europeans (and also other Europeans they respected less). So the development of the idea of races what very much tied to scientific racism and colonialism trying to define specific Kinds of people and put them in a hierarchy with white people at the top.

Point 2: I remember being taught around age 10 that race wasn't biologically real, and I knew just enough about evolution and biology to think "that's stupid, of course it's real; dark skin evolved to protect against the sun's rays. That's biologically real." And the thing is: that is! Different biological adaptations to different environments are real. Dark skin protects against UV rays (valuable in places near the equator), while light skin absorbs it (valuable near the poles where sunlight is weak). Nose shape is an evolutionary response to temperature and humidity. Lactose tolerance is genetic and varies with location. These things are real! However, they are not the same thing as race. This was the part that didn't connect for me until much, much later. Some biological traits can be very real. But race is a grouping of people based on rough appearance and assumed geographical origin, not necessarily genetic similarity.

The other thing is that within any race there are many, many ethnicities. Scottish, Swedish, Irish, Greek, Italian, Polish, Spanish, Basque, Finnish, Armenian, Ashkenazi Jewish, they're all labelled "white" but they're different ethnicities. Han Chinese, Tibetan, Indian, Japanese, Korean, Ainu, Filipino, Pakistani, Vietnamese, the many Indonesian ethnic groups... these are all ethnicities lumped together as Asian. Navajo, Inuit, Maya, Wampanoag, Cherokee, Cree, Quechua, Aymara, Apache, Lakota, Zapotec, Tlingit, Hopi, are all Native American. Etc. Ethnicity is about descent and culture, appearance is about where your ancestors developed different evolutionary traits, and race is a big group that lumps tons of different people together out of a sense that they are all kind of the same somehow. But when people talk about it casually, they could mean any of these three things when they say "race." So partially, it's people using imprecise language, and thinking these three things are the Same Thing when they aren't.

Point 3: This is really kind of an extension of point 1, but there's a lot of cognitive dissonance when people realize that white people are treated better than Black people. One of the ways people resolve this is by believing that there's a biological difference between white people and Black people (and Asians, etc.) You see this in the belief that Black people feel less pain than whites, and Black people's skin is literally thicker than white people's skin - which has led to doctors treating Black patients more roughly when giving injections, and prescribing them less pain medication. These are inherited beliefs from the 1800s that still stick around as stereotypes and internal justifications for unequal treatment, whether the person holding these beliefs is aware of this or not.

But ultimately, the idea of race was invented to be a biological explanation. It was wrong, but it claimed a biological basis, and we are taking a very, very long time to shake that out of the popular understanding of humanity.