For what reasons, doesn't the West push for the inclusion of India as a member of United Nations Security Council? India is more powerful than France or Britain and India is against China and pro-West on most issues, so why won't Western countries push for the inclusion of India as a member of the UNSC?
Stability is the basis of the security council system. The inclusion and exclusion of countries from the security council is a consequence of the allies in world war two, not of "fairness" or "balance", and not even of "power" or "wealth".
Adding new permanent members would weaken France and Britain. Adding new permanent members would reduce the power of the existing five, so it is not in their self-interest. As permanent members have a veto, there is no need for extra members to vote against China.
And why India and not Brazil? Or for fairness should not Pakistan or Indonesia also be added. And Nigeria? Argentina? Germany and Japan? It is much easier to justify no expansion than an expansion.
And finally, since China has a veto, no new permanent members can be created without Chinese approval.
Proposing India would harm the existing 5, upset the security system of the UN and be blocked by China (if not by the other four)