There is very little that binds people together and makes them a people than language. With languages going extinct at such a rapid pace (the stat is something like a a language dies every 14 days) mostly through repercussions of colonization. This was England's impact on Wales and it is very impressive that they've brought it from the verge to only vulnerable language status. All of these are interconnected and make for an emotive issue (and a very political one). People have fought very hard to get Welsh, Scots Gaelic, and BSL recognised and in schools (for the last, the fight still continues as it has yet to become a GCSE subject or even recognised in UK education as a Modern Language).
As for why, language gives a people an identity and an understanding of the people so learning it does both and both are important to creating a national identity (as are schools). Most would consider learning their cultural/national languages a very high priority, connecting with each other and their past.
Any language is useful and makes learning additional languages easier. I find the dismissive attitude towards Welsh and the push for other languages both sad and unrealistic. People living in Wales are far more like to run into a Welsh speaker or wish to read Welsh than Spanish or Mandarin. Sure, there are more Spanish or Mandarin speakers but due to dialects most cannot understand each other (you pretty much have to relearn the language to use it in Latin America compared to Spain Spanish which is taught in UK schools, for Mandarin it varies greatly by region and country to be be almost ununderstandable between them). For most careers/jobs, any language will be a bonus. Number of speakers shouldn't be the top priority in deciding a language, it's who we wish to communicate with.
And the argument of causing resentment was put for all modern languages and now the fall has been so great, and we so far behind global competitors, it's being brought back. The resentment argument has also been made for almost all subjects at one time or another. A nation has to decide how to define itself and this identity is put in the framework in schools to continue it - and Wales wants to continue it's language for all the reasons already discussed.
Really, I don't see why not.