Who should choose?

Not really having had any interest in the process until now, I was surprised to find that the eventual decision as to who should be leader of the Conservative Party (and therefore Prime Minister) rests with the members of that Party.  Because surely, this is just the situation which has caused all the problems for the Labour Party? And where is the logic?  As I see it, the general public choose, by way of the ballot box, who is the largest party in parliament and therefore form the government, and then it should be for the members of that party (i.e. their MPs) to choose who should be their leader. Otherwise you could end up - like the Labour Party have (twice now) - with the ridiculous situation where the leader of the party is not the choice of the majority of the MPs.  Bit like the captain of a football team being chosen by the fans, irrespective of what the manager or the players want.