IPA: /ˌdɪs.pjuːˈteɪ.ʃəs.li/
KK: /dɪsˌpjuːtəˈʃəsli/
In a way that is likely to cause disagreement or argument.
The students debated disputatiously, each trying to prove their point.
Disputatiously → It is formed from "disputare" (meaning to argue or debate) and the suffix "-ously" (meaning in a manner of). The word describes a manner of engaging in argument or debate.
Think of someone who argues or debates ('disputare') in a certain way ('-ously') — that's why disputatiously means in a manner that is argumentative.