Just to clarify, are you talking about "Russia"/the USSR during the time period of the formation of NATO (that is, in the Cold War context); or in the period after the breakup of the Soviet Union, when Russia became an independent state?

If you are talking about Cold War Russia (USSR), it's because they could not have even if they wanted to. The North Atlantic Treaty Organization was founded to contain the spread of Communism. There were serious fears that there would be war between Soviet Russia and the capitalist nations. In the early years of the organization, it was an almost entirely anti-Soviet alliance, and so for the Soviets to be allowed to join NATO would have been completely against the entire purpose of the organization.

The USSR offered to join Nato in 1954, but was rejected on the grounds that its inclusion would be contrary to the alliance's liberal political foundations and would allow a potentially disruptive Soviet veto.

It's likely that at least the last consideration played a part in the 1990s, as the alliance moved toward eastern European membership: Russia was just too much to incorporate with its size, its differing perspectives, the vastness of its potential security entanglements and the history of distrust on both sides.