Bryan Chapell wisely comments:
We struggle with these commands to 'avoid . . . dissensions' because we know there are things worth disputing, and because it seems divisive to separate from divisive people.--R. Kent Hughes and Bryan Chapell, 1 and 2 Timothy and Titus: To Guard the Deposit (Crossway, 2000), 364
Two perspectives may help.
First, Paul is speaking about ministry priorities. His words require us to examine whether controversy and argument about secondary issues become primary concerns in our ministries. If so, then our priorities require realignment.
Second, there is a difference between needing to divide and loving to divide. A divisive person loves to fight. The differences are usually observable. A person who loves the peace and purity of the church may be forced into division, but it is not his character. He enters arguments regrettably and infrequently. When forced to argue, he remains fair, truthful, and loving in his responses. He grieves to have to disagree with a brother. Those who are divisive by nature lust for the fray, incite its onset, and delight in being able to conquer another person.