Even from Brits' standpoint, India supplying 12 of the 4+ gen fighters is a better deal than to have Chinks make inroads into S.Americas with defence hardware. However, optics management can be difficult for the government- on the one hand they have some comprehensive economic program going on, and on the other India as a partner is selling military hardware to their Falklands rivals.
P.S- I mentioned Brits standpoint for a reason. Please don't comeback with "but Brits supplied shit to Pak", we all know that but Brits don't consider anything wrong in it. There are a lot of fundamental differences between the both our standpoints- they see Pakistan as a necessary hedge against India, there is a sizeable influential Pakistani community (that works for the interests of Pakistan, unlike a lot of Indian mofos), a penchant for sucking upto Islamists prevalent all over the liberal sphere especially the UK, and the good old "Divide and Rule" in the name of "balance of power", "rules based world order", and other convenient phrases in English as such.If there is an economic feasibility of supplying these jets to Argentina, imo, India must go ahead with it even if HAL's not to make any money out of it immediately. A few heartburns in the UK Parliament are manageable affairs