The clearest statement of the reason is about as unclear as can be imagined! It's the speech of Puigdemont. The right to independence is moral, cultural, economic and political. So now we all know!
The concept of self determination is usually regarded as a ius cogens, a compelling law, something which goes beyond the law or constitution of any nation state. I'm interested to note that posters on this board do not seem to feel that their own constitutions reflect this (USA and Germany). This may well be right. USA is an oddity in matters of constitution because the USA has the doctrine of American exceptionalism, and I'm inclined to leave it out now. However most EU nations do seem to have the idea that national identity somehow trumps self-determination, unless there is some sort of special case where the nation is persecuting a minority.
I suspect we are back to yet another clash between different legal systems and different ways of thought. The Civil Law system of Spain and in effect of the EU probably does say that the referendum is illegal, the constitution must be upheld, that Catalonia may not leave Spain. A Common Law system would give priority to self determination. Within the UK (and Canada) there is no possible doubt that a territory has the right to leave, and referendums in Scotland and Quebec have demonstrated this concept in action.
Quite why the Catalans want independence doesn't really matter if the right to self determination is prioritised. Within Common Law that right would be the starting point. I think separating the economies would take many years, so I think there are practical difficulties, but difficulties can be resolved.