The Americans did. They wanted to see if people could function in space as well as if they could bring them back safely. The Russians just sent a a dog with monitors attached and left it in orbit.
It is actually not true; the Soviets did test Vostok with animals before Gagarin. The first launches of Vostok were either with no crew or with animals that were recovered alive.
What you are refering to is Sputnik-2, which happened a few years before (1957) and technology then was simply not there yet for recovering a capsule.
https://en.wikipedia.org/wiki/Korabl-Sputnik_2
And the Soviet space program was very advanced by the standards of 1960s; this was a cold war necessity as the Soviet Union needed a vehicle to successfully deliver an atomic bomb to Continental USA. The US in the other hand, had a massive fleet of strategic bombers and therefore rocket technology was not a strategic priority. Hence, the US did not have anything close to the R-7 family of rockets (Sputnik, Vostok, etc) until the Saturn rocket of the mid 60s finally close the gap and won the moon race.
But by the early 50s Soviet original designs had greatly improved the German V-2 blueprints, and Soviet rocket designers like Sergei Korolev had already surpassed any former Nazi scientific.