This is the 2944th most frequent Russian word.
выступая
"Выступая" means "speaking" or "performing" (while addressing an audience).
In this sentence, 'выступая' is a gerund expressing the action 'speaking' or 'performing' described as ongoing during the action of 'he talked.'
Выступая на конференции, он рассказал о своём новом проекте.
Speaking at the conference, he talked about his new project.
Here, 'выступая' indicates her role of 'speaking' or 'representing' the organization while she performed the action of 'conveying greetings.'
Она передавала приветы, выступая от имени своей организации.
She conveyed greetings, speaking on behalf of her organization.
'Выступая' in this case expresses the activity of 'opposing' which specifies the context in which 'they presented arguments.'