But if ye have bitter envying and strife in your hearts - If that is your characteristic. There is reference here to a fierce and unholy zeal against each other; a spirit of ambition and contention.
Glory not - Do not boast, in such a case, of your qualifications to be public teachers. Nothing would render you more unfit for such an office than such a spirit.
And lie not against the truth - You would lie against what is true by setting up a claim to the requisite qualifications for such an office, if this is your spirit. Men should seek no office or station which they could not properly seek if the whole truth about them were known.

If ye have bitter envying and strife - If ye be under the influence of an unkind, fierce, and contemptuous spirit, even while attempting or pretending to defend true religion, do not boast either of your exertions or success in silencing an adversary; ye have no religion, and no true wisdom, and to profess either is to lie against the truth. Let all writers on what is called polemic (fighting, warring) divinity lay this to heart. The pious Mr. Herbert gives excellent advice on this subject: -
"Be calm in arguing, for fierceness makes
Error a fault, and truth discourtesy;
Why should I feel another man's mistakes
More than his sickness or his poverty?
In love I should; but anger is not love,
Nor wisdom neither; therefore g-e-n-t-l-y m-o-v-e."

But if ye have bitter envying and strife in your hearts,.... Though these may not be expressed by words, or actions: envy at the happiness of others, whether at the external blessings of Providence, as riches and honours, or at the internal endowments of their minds, as their wisdom and knowledge, their parts and abilities, is a root of bitterness in the heart, which bears wormwood and gall, and produces bitter effects in the persons in whom it is; it embitters their minds against their neighbours and friends; it is rottenness in their bones, and slays and destroys those who are so silly as to be governed by it; and also in the persons the objects of it; for who can stand before it? and strife in the mind, or an intention to strive end quarrel with others, who are the objects of envy, is very sinful, and of pernicious consequence: and if these be fomented and cherished in the minds and breasts of men, though they may not outwardly show themselves, yet
glory not; let not such boast of their being Gnostics, wise men, and endued with knowledge; they are far from deserving such a character; and such boasting is contrary to truth, yea, is lying against it, as follows:
and lie not against the truth; for, for a man to assert himself to be a wise and knowing man, and yet cherishes bitterness in his heart, and quarrelling and contention in his mind, arising from envy, at the equal or superior knowledge of others, he lies both against the truth of God's word and his own conscience, which condemn such things as ignorance, folly, and madness.

if ye have--as is the case (this is implied in the Greek indicative).
bitter-- Ephesians 4:31, "bitterness."
envying--rather, "emulation," or literally, "zeal": kindly, generous emulation, or zeal, is not condemned, but that which is "bitter" [BENGEL].
strife--rather, "rivalry."
in your hearts--from which flow your words and deeds, as from a fountain.
glory not, and lie not against the truth--To boast of your wisdom is virtually a lying against the truth (the gospel), while your lives belie your glorying. James 3:15; James 1:18, "The word of truth." Romans 2:17, Romans 2:23, speaks similarly of the same contentious Jewish Christians.

If ye have bitter zeal - True Christian zeal is only the flame of love. Even in your hearts - Though it went no farther. Do not lie against the truth - As if such zeal could consist with heavenly wisdom.