Almost by definition a debate is subjective. It is two people with opposing points of view about the same subject who are either trying to convince the opponent and/or the audience that what they believe about the topic is right. I'm not sure how you could have a single topic where multiple people have completely different views about the same topic and consider that objective.
People tend to attract to things that make themselves happy. Philosophers agree that the goal of humanity is to produce happiness. Morality makes everything fair, and if everything is fair, than everybody(yourself) is happy, If someone disagrees with your way of achieving happiness , than you will have a argument.
The logic need not change for the responses to change. That's why audience is such a huge factor and consideration for your audience is imperative to giving speeches. The same words in different contexts will produce very different results but ultimately debate itself and logic itself have nothing to do with emotions.
Debate is NOT subjective because all the research has to be done before the debate and all the facts need to be supported by facts in order to be counted valid in a debate in order to be able to be given points also If suppose it was subjective then people would have a hard time finding evidence for the debate.