See how both sides can be wrong?

It's good that you recognize that this is your opinion, and not fact.

In the 1990’s Gorbachev was promised no further eastward expansion of NATO

Because the claim is utterly false. Not only is there no written agreement promising that, if there was, it would itself be contrary to the NATO charter. Article 10 of the North Atlantic Treaty states:

The Parties may, by unanimous agreement, invite any other European State in a position to further the principles of this Treaty and to contribute to the security of the North Atlantic area to accede to this Treaty.

And to really get down to brass tacks, the idea that Gorbachev was promised no further eastward expansion of NATO is a lie, as stated by none other than Gorbachev, himself:

RBTH: One of the key issues that has arisen in connection with the events in Ukraine is NATO expansion into the East. Do you get the feeling that your Western partners lied to you when they were developing their future plans in Eastern Europe? Why didn’t you insist that the promises made to you – particularly U.S. Secretary of State James Baker’s promise that NATO would not expand into the East – be legally encoded? I will quote Baker: “NATO will not move one inch further east.”

M.G.: The topic of “NATO expansion” was not discussed at all, and it wasn’t brought up in those years. I say this with full responsibility. Not a singe Eastern European country raised the issue, not even after the Warsaw Pact ceased to exist in 1991. Western leaders didn’t bring it up, either. Another issue we brought up was discussed: making sure that NATO’s military structures would not advance and that additional armed forces from the alliance would not be deployed on the territory of the then-GDR after German reunification. Baker’s statement, mentioned in your question, was made in that context. Kohl and [German Vice Chancellor Hans-Dietrich] Genscher talked about it.

Everything that could have been and needed to be done to solidify that political obligation was done. And fulfilled. The agreement on a final settlement with Germany said that no new military structures would be created in the eastern part of the country; no additional troops would be deployed; no weapons of mass destruction would be placed there. It has been observed all these years. So don’t portray Gorbachev and the then-Soviet authorities as naïve people who were wrapped around the West’s finger. If there was naïveté, it was later, when the issue arose. Russia at first did not object.

Mikhail Gorbachev: I am against all walls - Russia Beyond

You may or may not see the further issue regarding any such promise that Russian propagandists allege might have been made, so let me explain: the treaty in question did not even involve NATO as a distinct polity, but was between The Federal Republic of Germany, the German Democratic Republic, the French Republic, the Union of Soviet Socialist Republics, the United Kingdom of Great Britain and Northern Ireland and the United States of America, as the treaty stated:

Having regard to the rights and responsibilities of the Four Powers relating to Berlin and to Germany as a whole, and the corresponding wartime and post-war agreements and decisions of the Four Powers;

The disposition of forces in Germany was a decision to be made involving the unifying governments of Germany, as West Germany had been a member of NATO. It had nothing to do with NATO expansion into the then-existing Warsaw Pact.

Russia has used that broken promise as an excuse to invade Ukraine.

Russia has used a lie as an excuse to invade Ukraine. This is where it’s important to be mature enough to separate fact and opinion.

See how both sides can be wrong?

It's good that you recognize that this is your opinion, and not fact.

In the 1990’s Gorbachev was promised no further eastward expansion of NATO

Because the claim is utterly false. Not only is there no written agreement promising that, if there was, it would itself be contrary to the NATO charter. Article 10 of the North Atlantic Treaty states:

The Parties may, by unanimous agreement, invite any other European State in a position to further the principles of this Treaty and to contribute to the security of the North Atlantic area to accede to this Treaty.

And to really get down to brass tacks, the idea that Gorbachev was promised no further eastward expansion of NATO is a lie, as stated by none other than Gorbachev, himself:

RBTH: One of the key issues that has arisen in connection with the events in Ukraine is NATO expansion into the East. Do you get the feeling that your Western partners lied to you when they were developing their future plans in Eastern Europe? Why didn’t you insist that the promises made to you – particularly U.S. Secretary of State James Baker’s promise that NATO would not expand into the East – be legally encoded? I will quote Baker: “NATO will not move one inch further east.”

M.G.: The topic of “NATO expansion” was not discussed at all, and it wasn’t brought up in those years. I say this with full responsibility. Not a singe Eastern European country raised the issue, not even after the Warsaw Pact ceased to exist in 1991. Western leaders didn’t bring it up, either. Another issue we brought up was discussed: making sure that NATO’s military structures would not advance and that additional armed forces from the alliance would not be deployed on the territory of the then-GDR after German reunification. Baker’s statement, mentioned in your question, was made in that context. Kohl and [German Vice Chancellor Hans-Dietrich] Genscher talked about it.

Everything that could have been and needed to be done to solidify that political obligation was done. And fulfilled. The agreement on a final settlement with Germany said that no new military structures would be created in the eastern part of the country; no additional troops would be deployed; no weapons of mass destruction would be placed there. It has been observed all these years. So don’t portray Gorbachev and the then-Soviet authorities as naïve people who were wrapped around the West’s finger. If there was naïveté, it was later, when the issue arose. Russia at first did not object.

Mikhail Gorbachev: I am against all walls - Russia Beyond

You may or may not see the further issue regarding any such promise that Russian propagandists allege might have been made, so let me explain: the treaty in question did not even involve NATO as a distinct polity, but was between The Federal Republic of Germany, the German Democratic Republic, the French Republic, the Union of Soviet Socialist Republics, the United Kingdom of Great Britain and Northern Ireland and the United States of America, as the treaty stated:

Having regard to the rights and responsibilities of the Four Powers relating to Berlin and to Germany as a whole, and the corresponding wartime and post-war agreements and decisions of the Four Powers;

The disposition of forces in Germany was a decision to be made involving the unifying governments of Germany, as West Germany had been a member of NATO. It had nothing to do with NATO expansion into the then-existing Warsaw Pact.

Russia has used that broken promise as an excuse to invade Ukraine.

Russia has used a lie as an excuse to invade Ukraine. This is where it’s important to be mature enough to separate fact and opinion.