I am inclined to read the passages in the new testament that speak of "tongues" as speaking about languages because in Koine Greek when a writer wants to write about foreign languages he uses the expression "foreign tongues", for example,
Cretans and Arabians, we hear them telling in our own tongues the mighty works of God. Acts 2:11
The main passage that leads to people disputing about angelic tongues (languages?) appears to be
1 Corinthians 13:1 If I speak in the tongues of men and of angels, but have not love, I am a noisy gong or a clanging cymbal.
Commentaries over the centuries before the later part of the 20th century say things like the following about this verse and its context
the tongues of men] i.e. the languages of mankind.
and of angels] The Rabbis speak of the languages of angels. It is possible that St Paul may be referring to this notion. But he himself also speaks (2Co 12:4) of hearing ‘unspeakable words which it is not lawful for a man to utter,’ when he was ‘caught up to the third heaven.’
and have not charity] Tyndale (who is followed by Cranmer and the Geneva Bible), love; Vulgate, caritas. The force of this eloquent panegyric on love is impaired, and the agreement between the various writers of the New Testament much obscured, by the rendering charity, instead of love. See note on ch. 1Co 8:1. The aim no doubt of the Vulgate translators was to avoid the sensuous associations which the Latin word amor suggested. But the English word charity has never risen to the height of the Apostle’s argument. At best it does but signify a kindly interest in and forbearance towards others. It is far from suggesting the ardent, active, energetic principle which the Apostle had in view. And though the English word love includes the affection which springs up between persons of different sexes, it is generally understood to denote only the higher and nobler forms of that affection, the lower being stigmatized under the name of passion. Thus it is a suitable equivalent for the Greek word here used, which (see Dean Stanley’s note) owes its existence to the Bible, since it does not appear in Classical Greek, and is first found in the Septuagint translation of the O. T.
sounding brass, or a tinkling cymbal] So Wiclif and Tyndale. The Apostle refers here to Psa 150:5, where the Hebrew speaks of ‘cymbals of sound’ and ‘cymbals of clangour,’ and the Septuagint renders almost by the same words as St Paul. Cf. ch. 1Co 14:7, where the difference between an unmeaning noise and real music is spoken of.
(The Cambridge Bible Commentary; Published 1882-1921)
Commentators since the 1990s are more inclined to allow the possibility that tongues in chapters twelve through fourteen of First Corinthians can mean "ecstatic speech" which many interpret to be sounds that do not constitute speaking in any language either human of angelic.
The matter is still hotly debated but it ought to be noted that a great many Christians claim to speak in tongues today and regard it as an exercise of a spiritual gift from God. It is, in my experience, difficult to get a clear consensus supported description of what happens when speaking in tongues and what "speaking in tongues" means but at the same time is it easy to get agreement from those who practise "speaking in tongues" that it is a gift from God and that many receive it.