>>>>In an attempt to hold our ground, my captain also sped up.....<<<<

Either your Captain should have kept his original speed because he thought it was the right and correct speed to taxi and so what if SWA got to the runway first ......or he should have taxied at his new speed to begin with because apparently he thought this new speed was an acceptable speed to taxi. If he thought it was perfectly ok to speed up, apparently he could have been taxiing faster to begin with. If he was taxiing so slowly that he decided to speed up when he saw SWA then I can't blame SWA at all. I have no problem taxiing a 737 at 25kts a long dry straight taxiway, meanwhile other guys are creeping along unnecessarily at 8 knots as if they are on ice. I see no speed limit signs on taxiways. Good for SWA. Perhaps if your Captain had not speeded up at the last second it wouldn't have been so close, but again -- if your Captain thought it was perfectly ok to speed up then, apparently he could have been going faster the whole time to begin with. Good for SWA.

Oh...and "V-1 - 10" and "we slammed on our brakes" are assurdly exagerrations. Wouldn't have been close if your Captain hadn't decided to speed up at the last minute.