There is little antithetical contrast in this beatitude. Both sides of the equation appear to provide something that is desirable: the pure in heart and seeing God. The universal meaning for most audiences comes from the causal connection between purity of heart and the ability to see God.
In the context of second temple Judaism, however, “purity” probably has a different meaning. Seeing God is obviously out of the reach of most mortals but it was a possibility at least once a year for the high priest who entered the temple’s Holy of Holies to offer sacrifice for his own sins, then for the people’s. On that sacred occasion, he entered Yahweh’s presence and thus had the possibility of “seeing” God. His position and ritual purity was a requirement for entering that room.
The key to this beatitude is understanding that “pure in heart” is an allusion to Psalm 24:3–4, which Jesus’s listeners certainly would have picked up:
Who shall ascend into the hill of the Lord? or who shall stand in his holy place?
He that hath clean hands, and a pure heart; who hath not lifted up his soul unto vanity, nor sworn deceitfully. (Ps. 24:3–4)
Jesus’s listeners would have also understood the context. Those with clean hands and pure hearts are those who are worthy to ascend “the hill of the Lord” and “stand in his holy place.” Both phrases are references to the temple. This beatitude is a literary reworking of the psalm, reversing its question/answer order to fit the beatitude format. Therefore, those who lack the high priest’s ritual purity will still “see” God because they are genuinely pure in heart, not just ritually pure. The restriction of ritual purity and Levite lineage is removed, and the temple is opened to all having individual purity.
Comparison: The Book of Mormon specifies “all the pure in heart” versus Matthew’s “the pure in heart.” The change is minor, simply fleshing out the text’s implicit meaning. It could have been a slip of the tongue during the dictation as easily as a purposeful addition.