Yogacara and Vasubandhu etc deny that matter exists by itself but rather that is comes from awareness and is merely a perception of the mind.what are the arguments Yogacarins make to prove their main thesis?
They don't believe that. That's an almost universal misunderstanding. Yogacara doesn't make any ontological statements about the universe, perception, reality, and so forth. Their approach was strictly soteriological. They were exclusively concerned with liberating the mind, not with describing things as they are. What Yogacara is concerned about is how the mind (store house consciousness and "I-making" consciousness) "perfumes" and "transforms" the sensory gates and how that in turn impacts perception. You aren't seeing a chair, for instance, but rather your entire life history, memories, prejudices, etc. dealing with chairs. That means that the chair you see isn't the same chair that someone at, say, the Buddha's time would see even if you were looking at the same object. Something that you might take to be a pretty shoddy looking recliner, after all, might be a veritable throne to them!
This has very real implications when it comes to liberation. Our personal histories impact not just our existential lives but even the very way we deal with and perceive the world. Our habituated, unenlightened perception makes us miss so much of what's actually there. We don't see the spaces between things, we don't perceive the energy, and we are wholly negligent of the emptiness that is always there. Hell, we don't even hear properly. Yogacara training (especially as manifested in Zen koan study) seeks to reacquaint us with what we are missing...not to assert any concepts regarding the nature of reality.
Objects or entities or individual phenomena are delineated according to our (learned/acquired) interpretative framework.
Their delineation depends on the scale of observation and the chosen evaluation criteria. They don't exist delineated ontologically.
Same for the concept of "matter". It's just one way of seeing/describing what could be described as e.g. wave functions. None of these descriptions is ontologically primary. Hence, everything we can observe and talk about are concepts existing in our mental space, referring to reality, approximating reality - but in actual reality you can't unambiguously nail down "objects" and "matter" - real things are a bit more amorphous and complex.
This is called vijnapti-matra (Representation-Only). The Wikipedia article on Yogacara does a pretty good job summarizing various experts comments on the topic: https://en.m.wikipedia.org/wiki/Yogachara#The_doctrine_of_Vij%C3%B1apti-m%C4%81tra