In his autobiography, Benjamin Franklin advised on how to keep friends and influence people:
“I took delight in it, practiced it continually, and grew very artful and expert in drawing people, even of superior knowledge into concessions the consequences of which they did not foresee, entangling them in difficulties out of which they could not extricate themselves, and so obtaining victories that neither myself nor my cause always deserved. I continued this method some few years but gradually left it, retaining only the habit of expressing myself in terms of modest diffidence, never using when I advance anything that may possibly be disputed the words, “certainly,” “undoubtedly,” or any others that give the air of positiveness to an opinion; but rather say, “I conceive or apprehend a thing to be so or so,” “It appears to me,” or “I should think it so or so, for such and such reasons,” or “I imagine it to be so,” or “It is so if I am not mistaken.”
If you desire instruction and improvement from the knowledge of others, you should not at the same time express yourself as firmly fixed in your present opinions; modest and sensible men, who do not love disputation, will probably leave you undisturbed in the possession of your error. In adopting such a manner you can seldom expect to please your hearers, or to persuade those whose concurrence you desire.
You need to pick your battles and you would be well advised to follow Franklin’s counsel when engaging with a colleague. If someone has built a career and a reputation on a particular idea which you believe is wrong and you set out to prove why you can expect an aggressive response because you’ve effectively challenged the value of their life. Challenging colleagues on minor issues that are not earth shattering and may in fact help you clarify and strengthen your own view can be extraordinarily helpful but if you prove them wrong, even if only in your mind and on the basis of your view of the evidence, you need to prepare for combat.