Two Opposite Meanings of 'Cleave'?

Solution 1:

OED does differentiate the etymologies:

s.v. cleave, v.¹

1. a. trans. To part or divide by a cutting blow; to hew asunder; to split.

Etymology: Common Germanic: Old English clíofan, cléofan, past tense cléaf, plural clufon, past participle clofen . . .

s.v. cleave, v.²

1. To stick fast or adhere, as by a glutinous surface, to . . .

Etymology: Old English had two verbs; clífan strong (* cláf, plural clifon, clifen), and clifian, cleofian weak (clifode, -od ).

Biblically enjoined to “cleave unto his wife,” poor Henry VIII appears indeed to have got sadly confused between these two senses, though curiously not in the case of wife #4.