Big 'A' - "Agile" is waterfall re-branded - an excuse for corporate empire building and business as usual. It involves lot's of meetings and not trusting those who build software to do the right thing.
Small 'a' - "agile" is the implementation of the manifesto, which basically comes down to smart people figuring out how to work together towards a goal, often by taking small steps.
Until the terminology is sorted out the discussion can't help but be confused.