Imagine that some of these candidates were very similar to one another. I may have voted for John, but Julie would have been good enough--certainly better than Frank or Sally whom the House just voted in. If we took John's and Julie's votes and combined them, they could have had 30% instead of 15% each. If we find a few more candidates to merge with, we could have all agreed to vote on this one person and received more than 50% of the votes to swoop in for the win. It may not be each of our first pick, but it is certainly better than having no voice at all when the House votes on our behalf! So people of like mind X pooled their resources to vote for a strong X-oriented candidate. These are the issues we collectively care most about and X will help us unite our votes.
Of course, those who care strongly for the opposing viewpoints will then do the same thing lest they become voiceless in the race. So they pool their resources to make candidate Y. If, by chance, there are other viewpoints not well shared with X or Y, they could make Z. But now, the votes are no longer going to be 49% to 51% with a clear winner, we are going to get 25%, 30%, and 45% (for example). No majority winner of 50% or more. So once again, the house gets to pick for us because we as a people could not make up our minds. The House preferred the guy who got 25% and now the least-desired of the 3 gets voted in. Well that's certainly not desired since the Zs would have much preferred X over Y and now 75% of the population is left extremely unsatisfied.
As long as it requires more than 50% of the votes to become president and we can only vote for one person, we will be forced into a 2-party system. Absolutely guaranteed. It is simply the smartest thing that smart people can do: unite their votes. Any division past 2 people will destroy any chance of the people picking their own president. Thus, if you do not like the 2-party system, we must find a new method of voting that does not permit only a single vote or which does not require a >50% majority.
With the technology we have today, it would not be hard to come up with a better system of voting. We could vote for our top five favorite candidates in order of desire and have an algorithm find the winner. I want Frank, but I'd be down with Sue if not enough people agree on Frank. Lo and behold, this form of voting has already been invented. It is called Single Transferable Voting. The basic idea is "if it can't be Frank, then transfer my vote to Sue." Everyone wins, no wasted votes, you vote your true conscious, you get someone who best represents the people. So rather than voting third party, let us combine our votes for now to prevent a catastrophe and then push the agenda for voting reform which is the only way to break the 2-party system.