I think if you have an ounce of empathy, it's very easy to understand why and how the participants sometimes become emotional.
They're outside their comfort zone (for the most part, anyway), which heightens stress.
They're constantly being exhorted by the judges to "don't just do the steps, lose yourself in the dance" and "find the connection with your partner" ie encouraged to engage their emotions in the process.
They're in various stages of physical and mental exhaustion.
Post-dance they're full of adrenaline which has to disperse somehow.
They know, as much as anyone, that this is a popularity contest as much as it is about dancing. They've put themselves out there, not just in the 90 seconds of the dance but in the ITT interviews, the training footage, effectively saying "this is the real me...like me!". Each light going off around them while they're getting closer to the dance off must feel like a little segment of the audience saying "nah...don't like you".
Given all that, I'm amazed that more people don't cry, male or female!