Different people will have different answers to this question. I will give an argument for and an argument against the idea that the first past the post system is unfair. You can look at these arguments and decide which one you agree with.
Some people would say that the first past the post system is fair. They would argue that whoever gets the most votes should be the person who is elected to office. After all, they would say, democracy is supposed to be about majority rule. The candidate who gets the most votes has the support of the most people and therefore should be the one elected. This is an eminently fair system.
On the other hand, some would say that this system is unfair because it ignores the voices of the people whose candidate did not win. These people would ask why (for example) the voices of the 55% of the voters who choose one candidate should be heard while the voices of the 45% who voted for a second candidate should be ignored. This is surely unfair to the people whose candidate does not get the most votes. Those people deserve to be represented as well. Therefore, the first past the post system is unfair.
Which of these arguments makes the most sense to you?