The same proper exegesis that establishes important Christian doctrines such as the deity of Christ, the Trinity, justification through faith alone, etc. establishes definite atonement (along with all the doctrines of grace).
Yet ironically, I continue to see far too many ‘Calvinists’ use the same practices as that of the followers of Arminius at Dort when addressing Arminianism—namely, providing bucket loads of refutations, but then being absent (and/or very sloppy) in presenting positive exegetical affirmations from the text of Scripture.
Even worst is when misguided “Calvinistic” apologists rely on and employ philosophical apologetics and erroneously use Matthew 23 as a hermeneutic to evangelize and thunderbolt their typical myopic agenda in refuting the false system of Arminian autosoteric.
In fact, Arminianism promotes several unbiblical views including universal atonement, conditional election, and, with some, partial depravity. However, we as Christians, who correctly understand and embrace the doctrines of grace should (as mandated) confront these errors appropriately and out of love using the exegesis of Scripture to both affirm important biblical doctrines and refute any false doctrines whether essential or tangential.
Scripture is sufficient to affirm and refute false doctrines.