Is this so? Let’s call the statement above P0.
Let’s start from first principles. A discussion is performed by agents (peer interlocutors, a speaker and its audience, etc). I believe we can make it an axiom of our discussion that there are at least two sentient agents involved. Assume two (A1 and A2), without loss of generality. Focus on one of them, A1.
A1 joins the discussion in pursuit of a goal G1, and for that purpose puts forward an argument, as does A2 in pursuit of G2. G1 and G2 might or might not be the same.
Lets not concern ourselves much with the mechanics of the argument, but with the goals and their relation to P0.
Focusing on A1 and G1, it its trivially true that if G1 involves convincing A2 of some fact F, then P0 is trivially false except in the specific case in which A2 is the sort of agent which can only be convinced by a purely logical argument.
Empirically, most humans are not such agents.
Unproven conjecture: No human is such an agent.
Empathic communication (communication relating to feelings) is known to be an effective tool in convincing human agents [1].
Therefore P0 is invalid, arguments based on feelings are likely to have a use in discussion when the goal is to convince.
Let’s, however, assume that G1 is the goal of the idealized logician, to “arrive at the truth, whatever it might be.” Two cases arise:
Either A1 holds all the facts and the means of reasoning required to arrive at the truth, in which case communication with A2 is unnecessary. Or else A1 requires information or processes from A2 to arrive at the truth.
In the later case, if G1 == G2, meaning both agents seek the truth as their primary (perhaps only) objective, and this remains true through the whole discussion, then P0 could apply, under those strengthened premises.
However, if the goal of A2 is not initially the pursuit of truth, or if G2 ever changes after becoming the pursuit of truth, then A1 must attempt persuasion on A2 to (re-)align their goals. This could benefit from an emotional argument.
And this is all assuming A1 has the pursuit of truth as its only goal, and not, say, a performative goal of showing its command of logic, at the expense of the optimal process for arriving cooperatively at the truth. It also assumes that persuasion from one agent might not be used to move the other closer to the truth, or more receptive to future logical arguments, which might be possible in situations where the agent’s internal process is not perfectly logical (consider e.g. the practice of psychotherapy).
As a side note, when the goal G1 is performative, an emotional argument can be cloaked in the language of logic, for example the argument put forward by A1 might on the surface be about the subject of discussion, while intending in truth to convey information about A1’s social standing, for example, to show off education or intelligence by means of elaborate language not otherwise needed to make the argument persuasive or logical (e.g. [2]).
Other possible goals include, e.g. the didactical, the parodical, or that of artistic expression.
[1] https://pdfs.semanticscholar.org/b879/4bf1a7e6845f87824c52a3...
[2]