Sanskrit works on philosophy are full of arguments with rival schools. And there is one point in these arguments that seems a bit puzzling. It was quite natural, that one tried to dismiss the rival opinion. And of course the best way to do it, was to demonstrate the logical inconsistency of the opponent’s theory or the fallacies in his argumentation. Still it was not rare, that the real reason for the opponent to hold his opinion was not in the defects of his reasoning. Different schools discussed the same problem from different points of view, relying on different backgrounds.
E.g. the Vaiśeşikas claimed, there are two types of relation (samavāya and saMyoga), because they had to explain permanent ontological relations (e.g. of dravya and guņa) on the one hand and unstable relations (e.g. relations of the atoms) on the other. Semantic relation initially was not interesting for the Vaiśeşikas. But once they had to express their opinion on this subject, they claimed, semantic relation did not exist. The only reason for this claim was, that the existence of semantic relation did not fit their realist world-view.
Still the opponents of Vaiśeşika (Bhartŗhari, Dharmakīrti), while arguing on relation, never tried to understand the real reasons for postulating such views. They just used some of the Vaiśeşika’s statements extracted from the context, bringing them to regressus ad infinitum etc.
It seems to me, this mode of arguing dominated in Indian philosophy. Bhartŗhari sometimes tried to understand the reasons of his opponents to hold this or that opinion, but this was most probably because of the inclusivist tendency of Grammar (sarvapārşadaM hīdaM śāstram). Perhaps the Jain anekāntavāda was another exception of the rule.
And how do you experience the way Indian philosophers dealt with rival ideas?