If China is so concern about UK. It would have long stop supporting Argentina claim of falkland.Back to the topic, selling JF-17 to Argentina will result in objection from UK&Brazil. Since that Pakistan is a member of the Commonwealth and that China-UK currency-swap is going on, the expense may be high, let alone plus the objection from Brazil.
What can PK&CN benefit from the deal may be only about 1-2 billion $ and political/economic/millitary tie with Argentina.
But if we sell the aircrafts, UK may make some noise on HK&TW&Tibet issues, and support India in some aspects against PK, all these above are bothersome BS. Also Brazil won't stay silent.
UK and Brazil are powers, we must take them into consideration.
What's more China has already cooperate with Argentina AF on helo Z-11.