It is always a challenge to deal with people who are illogical. You might identify them as illogical, but they may be unaware. Instead of getting emotional or angry about the situation, use your intellect to counter their faulty logic to get them back on track.

Once you feel like you are making headway in the conversation, gauge how successful the argument is by paying attention to the kind of response you get from your opponent – if they seem more open-minded then continue debating further, but if there is no change in their demeanor, move onto another topic.