Ground crew suggesting I am lying x3 times

I was booked on flight FA 232 to PE on the 8th of March. We were going to depart via gate E5 so I seated myself in front of the gate. Long story short was that I was told that I had missed my flight when I went to the front of the gate. I did not understand how that had happened as I was sitting right there. A lady assisted me and her college then told me that it could not have been in a manner that I did not like, suggesting that I was lying. He then said that I must have been late and I said to him no that I was not 16:05 there when boarding started but no later than 16:09. Again he suggested that I was lying and this time I told him that he should not do suggest that I am lying I don't like that. Again he suggested that I was lying and then I lost it and called him a AH (for which I am sorry)<br> Me missing a flight due to some confusion somewhere is fine I will take responsibility for it, but please, bad attitude and suggesting I am lying x3 times!! I did not deserve that. The help desk could not find me a suitable flight so I had to use Kulula.....could not move my flight to another date except the first flight the next morning so I lost the money on that flight.