There are no biblical references as to why Catholic exorcists say that Latin is hated by the Devil. Many Catholic priests who are exorcists have made this claim (statement). But I imagine that exorcists in the Eastern Rite Churches (Catholic or otherwise), have the Devil saying the same about their traditional liturgical languages also.
Here is what one article has to say on this subject:
I wanted to pass on one little comment that he made almost in passing. I do not know where he stands liturgically in regard to the Mass - there was nothing in what he said that led me to believe that he celebrates the Latin Mass, for example. However, he did explain that the Rite of Exorcism is only said in Latin. One reason is practical - there is no approved translation in English as yet. He gave another reason why he was so strongly in favor of the use of Latin in the Rite of Exorcism: “The Devil hates Latin, it is the universal language of the Church.” I asked him about this afterwards, and he repeated it, saying that his personal experiences as an exorcist who has performed many, many exorcisms have convinced him of this. He told me he had heard from exorcists who did exorcisms in Italian, Spanish and Portuguese (the only approved vernaculars for this Rite) that Latin was the most effective language. - The Devil Hates Latin, Says Exorcist
Until very recently (2014), an English translation of the rite of exorcism had not been approved by the Church. While the Vatican has approved translations of the rite in multiple languages, Latin seems to be the most effective during the course of exorcism. Thus Satan's hatred of Latin language.
Catholic exorcists are guarded in what they reveal about their exorcisms because as we all know that Satan is a liar from the beginning. Even in exorcisms, the priest will not readily believe the adversary and must not divulge too freely what was said in order to protect the identity of the victim.
And it came to pass, when the evil spirit from God was upon Saul, that David took an harp, and played with his hand: so Saul was refreshed, and was well, and the evil spirit departed from him. - 1 Samuel 16:23
The famous exorcist for the diocese of Rome, Fr. Gabriele Amorth, stated in one of his books that as David liberated the soul of Saul from the Evil Spirit of Melancholy, so to the power of Gregorian Chant has a great help in liberating the demon from persons and homes.
As Satan hates Latin, so too he hates the Sacred Music of the Roman Rite. Gregorian Chant is sung uniquely in the language of the Church: Latin.
Suffice to say, there is no sacred music in Hell.
This is why the devil hates sacred music so much. It reaches the depths of our soul and raises us up to the Heaven. It should be no surprise to us when a parish’s sacred music program is single-handedly dismantled. He will do all he can to prevent us from hearing the Divine Voice of God. - Why the Devil Hates Sacred Music
Although there is no biblical references for to support this claim (in question), there have been some cases where the Devil has made like statements during the course of an exorcism to a Catholic priest (exorcist). But we must always remember the Devil is a liar. I have heard this from several exorcists. Thus it is more than just an old notion