Those people have been supporting the cause for a while as the flag was pretty weather-beaten and faded. It's a complex issue, that's for sure.
Barcelona being a large, international city has (comparatively) more in common with Madrid and the rest of Spain - there is and has been a lot of national migration there, and of course it's an international destination for both tourism and business ... I've also learned that capital/large cities are not a good indicator for what a country is really like.
Valencia where I currently live is similar in that here in the city, the regional language (Valenciano - a variant of Catalan) is spoken a lot less whereas out in the towns and villages, especially as you head North towards Catalunya, it's much more widely spoken. On this short day trip to Tortosa I noticed the difference ... Catalan was the language spoken in the streets. It's spoken more in Barcelona than Valenciano is in Valencia but again it's the smaller towns where you notice that difference in language and identity that comes with it - these people often feel Catalan firstly, not Spanish. That said, I think few people really feel all that Spanish - there's far more regional pride than national pride throughout the country.
There are also economic arguments but those quickly become erroneous on both sides, in my opinion, and I'm already writing an essay here ... I would just say that while Barcelona is thriving and other areas of Catalunya may enjoy riches from tourism, industry and finance, it's not without its economically deprived areas or the sufferings of post-industrial decline either, nor other political hot potatoes such as national and international migration. Independence isn't a magic wand you can wave to solve everything.
The arguments against separatism are somewhat frustratingly limited (as was also the case with Brexit - and it was this lack of compelling argument against the ill-founded [at best] but attractive-sounding "we'll be able to have it all [just don't ask how exactly]" campaign that led to a disillusioned defeat) to "this is how it currently is so it should stay this way"; "the constitution (of the country you wish to separate from) says No" and "protecting the unity of Spain" as if Spain were some God-ordained (perhaps understandable what with the Nationalist Catholic dictator and all) and defined concept and had never changed ... which it has, albeit not all that recently. Independence or even vaguely sympathetic parties (like Podemos who wish to permit a referendum but would campaign against independence) are deemed Anti-constitutional by the political establishment. None of this helps calm the separatist sentiment.
That said, personally I think the world needs less borders and not more, so in that sense I'm kind of against separatism generally, even if I understand the motives of the people concerned and find the attitudes against it frustratingly simplistic, unsympathetic (as in, not making an effort to understand those motives) and limited.
Flag related jazz ... those Red and Yellow stripes come from the Kingdom of Aragon, whose flag to this day remains a simple set of five yellow and four red stripes. They feature in the flags of Catalunya and Valencia (as well as Spain itself) and reflect that these two regions were once part of the Kingdom of Aragon. Aragon and Castille were united by marriage in the late Medieval period forming the basis of what became Spain. They later re-conquered Andalucia.
My girlfriend has suggested that the whole Catalan debate would be less problematic were the language called Aragonese ... which in effect it is the remnants of, as these regions would have spoken a language distinct from Castellano, which became accepted as Spanish ... it's name reflects that it was the language of Castille though. Another argument levied against Catalan independence is that Catalunya was never a fully-formed nation of its own, merely a part of the Kingdom of Aragon. Were the name of its language a reflection of its Aragonese heritage, those claims might be easier to counter ... but despite being entirely valid, they're too easily dismissed because of mere nomenclature.
In conclusion: America First, Catalunya Second.
EDIT: I've had a quick read of the forum rules and it does say political discussions are not allowed and I might have gone a bit too Political in the Geo-Political/Geo-Historical ramblings above. I've tried not to be partisan ... especially because I don't consider myself to be partisan ... but if anyone feels like a line has been over-stepped I'm happy to either edit or have the post edited. Peace to all.