Why party loyalty leads to factionalism

Even though representation is broken down into constituencies... the mechanics of the first past the post system of voting (as compared against pr) are as though we are living in one giant constituency. We assume in any analysis that the party members are loyal to the party whips and there is complete discipline. Which is a reliable assumption given our experience. So then if constituency representation is determined by fptp then this will inevitably lead to a presidential-style system because of this discipline. The leader of each dominant party is the (de facto) leader of each constituency which that party holds. So in each constituency we are choosing between the leaders of the parties and not the actual direct representatives. If this is not the case it means nothing for a politician to join a party... in exchange for the ability to be the sole representative of the party in a seat the politician must give up loyalty to the party or leave. So we assume the politicians are loyal to their party. This being the case then each seat is a miniature version of the government as a whole and if one politician only is sent from each seat to parliament then we will have a presidential system. If there is not proportional representation at the constituency level then the government will not be proportional... because of the formation of political parties.