Hungary effectively opposed their membership, for instance, since 2018. According to the MFA of Hungary
Since 2018, Hungary has been blocking ministerial-level political meetings between NATO and Ukraine as a sign of protest over Ukraine violating the human rights of its ethnic minorities.
And more simple terms Reuters paraphrased sometime in 2019 that
Hungary’s foreign minister on Wednesday said Budapest would block Ukraine’s membership in NATO until Kiev restored the rights that ethnic Hungarians had before a language law curbed minorities’ access to education in their mother tongues.
I'm less sure what might have happened between 2015-2018. But the conflict in Eastern Ukraine was already ongoing even then. And I'm daring to quote from TASS on this, which probably is close enough to the source, a 2021 interview with the German ambassador to Ukraine:
The conflict in Donbass and the situation around Crimea, which Kiev considers Ukrainian, are obstructions for Kiev’s accession to NATO, German Ambassador to Ukraine Anka Feldhausen said in an interview for Ukrainian television on Friday.
"The fact remains - there is a military conflict in Ukraine. It is always difficult for NATO to accept new countries with such ongoing conflicts," she said.
When asked whether the conflict in east Ukraine and the situation around Crimea are obstructions for Ukraine’s membership in the Alliance, the envoy said "yes."
It is fairly correct to say that according to the principles laid out some decades ago, NATO will not easily consider membership of countries with active military conflicts.
States which have ethnic disputes or external territorial disputes, including irredentist claims, or internal jurisdictional disputes must settle those disputes by peaceful means in accordance with OSCE principles. Resolution of such disputes would be a factor in determining whether to invite a state to join the Alliance.
And the heavyweights of NATO were not exactly keen either...
“There are steps that Ukraine needs to take,” Jen Psaki, the White House press secretary, said in September after President Volodymyr Zelensky of Ukraine met with Mr. Biden in the Oval Office. “They’re very familiar with these: efforts to advance rule of law reforms, modernize its defense sector and expand economic growth.” [...]
“The principal objection would be: Does such a move actually contribute to the stability in Europe, or would it contribute to destabilization?” said Douglas E. Lute, a former U.S. ambassador to NATO. “I think it’s indisputable there wouldn’t be consensus among the 30 members, even though all allies agree that Ukraine has the right to aspire to become a NATO member.”