Basically, despite the victory of the CPC, you can't change society in an instant, and contradictions existed in Chinese society and politics that came to a head in the GPCR.

1. A socialist society requires people not be shackled by the subservient attitudes imposed on them by religion and bourgeois thought, such as confucianism and ancestor worship. This is one of the targets of the "Olds". It involved iconoclasm and targeting of individuals who espoused such ideas.

The good: while old customs persist in modern China, their influence of daily life is much diminished, leading to a freer society. The bad: loads of ancient artifacts were destroyed, and a shitload of people who were targeted by red guards were targeted for frivolous reasons, lots of innocents caught up in the fervour because someone didn't like you and said you were petit bourgeois or something.

2. The party had been infiltrated by liberals and revisionists, and the party in general had distanced itself from the masses, forming an elite class. Resolving this required purges, internal party struggles, and sending bougie kids to live alongside peasants.

The good: China didn't go the way of the USSR, so it must have done something, and sending privileged kids to do labour is cool. The bad: internal party struggles spilled over into the lives of the masses, who just wanted to grill; the definition of "Elites" included a lot of people who didn't really deserve it, and the turmoil of the time basically froze China in time until it ended (e.g. scientific research, industrial development etc. all put on hold).

At the very least, the hardline ultraleftist cliques that had formed in the party were purged, and after Hua Guofeng lost favour to Deng, set China on the current path its on today.

It remains to be seen if Deng can really be called China's Gorbachev, because to be fair, despite the revisionism, Deng wasn't an impressionable idiot like Gorby. Things are still up in the air though since Xi's last round of purges failed to get rid of the Shanghai liberal clique's influence, and once he goes we might get another Jiang/Hu, in which case its another decade of milquetoast keynesianism, business as usual I guess.

Final final edit for real this time: do not consider this a full picture of the cultural revolution, just stuff that's relevant to the point at hand. The intricacies of the leadup and aftermath and all the reasons it happened (gang of four, Mao being an old coot, revisionism in the USSR etc.) can fill up multiple volumes of encyclopedias.