Propaganda and sexist attitudes, as well as training and spacecraft design, were the big reasons. The Soviets were very good at exploiting ways to beat the USA in being the first to do things in space, and realized that women in the USA in the 1960s would NEVER be considered to be allowed as active astronauts, even if they had the skills.

The USSR realized that having the first man and first woman in space would forever be in the history/record books as a very big deal, and wanted to take advantage of that opening in the space race to score a propaganda victory that they could use to proclaim and show the toughness and sex equality of Soviet women to the world. Remember that it took the Soviets 19 years after Valentina to fly another female into space - Svetlana Savitskaya, who flew in 1982 - which shows they really did not care about the "equality" issue all that much, but rather the propaganda victory. The Soviets made a huge deal of Valentina's flight, publicly

The reason the USSR were willing and able to fly Valentina was because of the design of the Vostok capsule system. The entire flight of the Vostok system was designed to be controlled from pre-programmed on-board systems and the ground if need be, without any cosmonaut intervention actually needed at all. Valentina by all accounts had an absolutely miserable flight (nothing to do with her sex BTW, just she did not acclimate to the conditions due to inexperience), and her big skill in her being selected for that Vostok 6 mission was that she was an experienced parachutist - a requirement because the Vostok spacecraft actually ejected the cosmonaut prior to the capsule impacting the ground, with the cosmonaut landing under their own personal chute rather than in the spacecraft itself.

The issue of putting a woman's life at significant risk in the USA during the 1960s was a big deal (and seen as a big cultural no-no) in the military/space arena, and due to prevailing sexist attitudes at the time, the USA was worried enough about the PR disaster of losing a man in space, let alone the utter calamity that would result in losing a woman's life. It took until the 1980s, when America's STS shuttle program (with its large passenger capability) began to ramp up, for the USA to be willing to fly females.