I want to preface my answer by saying this answer from u/kieslowskifan is a comprehensive rundown to why the USSR did not produce aircraft carriers until the Admiral Kuznetsov was laid down in the early 1980s.

During the Second World War, specifically in the Pacific Theater, the United States Navy became increasingly effective in their use of what we now call Carrier Strike Groups (CSG). The predecessor to these groups in WWII were Task Force 11, Task Force 16 and Task Force 17. Task Force 16 under the command of Adm, Halsey and later Adm Spruance was made up of CV-6 and CV-8, the Hornet and the Enterprise respectively, escorted by a few cruisers and a handful of destroyers. The efficiency of TF16 was shown in the Doolittle Raids, Battle of Midway and the assistance provided at the Battles of the Eastern Solomon Islands and Guadalcanal campaigns.

The US Navy had a fleet drawdown from the end of WWII until Reagan’s 600 Ship plan in 1980. Many Pre-War ships were decommissioned in 1945 and 1946 with the remaining ships built during the War being decommissioned through the late 1940s and through the mid 1950s. The decommissioning of the Iowa Class of battleships signaled the change in naval warfare. The days of bombaring land based targets was gone, at least at the time. There were talks to refit the Iowa’s with nuclear missiles and other guided missiles but those failed.

Back to your question. The main reason was the ability for the carrier and the Carrier Strike Group to project power and control the seas. The US Navy was the strongest after WWII and has continted ever since. The can be used as a show of force, protect the economic area, provide humanitarian aid and most importantly be a floating military base capable of striking at any moment. The US focused on a blue water navy post war and the Carrier Strike Group fit the role perfectly. The USSR could not match the pace of the US Navy and turned to creating a defensive fleet of submarines.

The modern CSG consists of a super carrier, and air wing, usually two Aegis equipped guided missile cruisers (CG), a destroyer quadron for ASW and AAW, two fast attack submarines (SSN) and supply ships. A CSG alone is larger than some forgien navies.There are currently nine CSGs, 8 of which are stateside and one homeported in Japan. It comes down to power projection at the point. This can be seen today even as recently as Oct 2020 where the USS Ronald Reagan entered the South China Sea.

The Soviet Union simply could not afford to build carriers and the politics of building them got in the way. The USSR decided to shift its focus to counter the US Navy’s build up of carriers by outbuilding the USN in submarines. Between 1950 and 1958 the USSR is reported to have built a little over 200 Whiskey-class submarines.

A widely quoted explanation from Krushev where he said in a memoir “The Americans had a mighty carrier fleet - no one could deny that. I'll admit I felt the nagging desire to have some in our own navy, but we couldn't afford to build them. They were simply beyond our means. Besides, with a strong submarine force, we felt able to sink the American carriers if it came to war. In other words, submarines represented an effective defensive capability as well as a reliable means to launch a missile counterattack”

In short, the US moved towards carriers because they saw the effectiveness of them in battle as well as power projection while the USSR simply couldn't afford to make carriers.

Please let me know if you have any follow up questions or want specific sources.