On the other hand, they say that scholars' rivalry increases wisdom. Elijah the prophet too said, “I have been very zealous for the Lord.” And regarding Phinehas: “Phinehas son of Eleazar son of Aaron the priest has turned back My wrath from the children of Israel by being zealous with My zeal among them, so that I did not consume the children of Israel in My zeal. Therefore say: behold, I give him My covenant of peace. And it shall be for him and for his offspring after him a covenant of eternal priesthood, because he was zealous for his God and made atonement for the children of Israel.”

The Holy One, blessed be He, is also described as a jealous God.

And in the section of the suspected adulteress, the root for jealousy repeats several times:
“And the Lord spoke to Moses, saying: Speak to the children of Israel and say to them: if any man’s wife goes astray … and a spirit of jealousy comes over him and he is jealous of his wife, and she has become defiled; or a spirit of jealousy comes over him and he is jealous of his wife, and she has not become defiled … then he shall bring her offering for her … for it is an offering of jealousies, an offering of remembrance that recalls iniquity … And the priest shall take from the woman’s hand the offering of jealousies, and wave the offering before the Lord and bring it near to the altar … This is the law of jealousies: when a wife goes astray under her husband and becomes defiled; or when a spirit of jealousy comes over a man and he is jealous of his wife, and he shall set the woman before the Lord, and the priest shall do to her all this law. Then the man shall be free from iniquity, and that woman shall bear her iniquity” (Numbers 5:11–31).

The Talmud in tractate Sotah tries to clarify:
“Reish Lakish said: What is the meaning of the term warning? A matter that casts jealousy between her and others (between the woman and others) … And Rav Yeimar bar Rabbi Shelemya said in the name of Abaye: A matter that casts jealousy between him and her (between the husband and his wife). … Apparently they hold that it is forbidden to be jealous. And according to the one who says it is permitted to be jealous, what is the meaning of the term warning? Rav Naḥman bar Yitzḥak said: warning means nothing other than admonition” (2b).

Two approaches are represented in this passage.
The first interprets “to be jealous” and “jealousy” negatively, in the sense of strife. An action that creates social or personal tension. According to this view, jealousy is forbidden, and according to this view a “spirit of jealousy” is a spirit of folly (ibid.). So according to Reish Lakish and Abaye, two great Amoraim, it is forbidden to be jealous.
That is how Rashi explained the passage: “Jealousy—that is anger.”
By contrast, according to the second opinion, that of Rav Naḥman, the term means admonition and warning. According to this view, such warning is permitted, and it stems from a spirit of purity (ibid.).
In Jewish law it was ruled that the process explained in the section of the suspected adulteress cannot begin before the husband warned his wife and specified his suspicions to her. This warning must be given before two witnesses.
That is also how Rashi explained the biblical section, and so did Maimonides in the Mishneh Torah. In Maimonides’ words:
“Warning mentioned in the Torah … is that he says to her in the presence of witnesses: Do not seclude yourself with so-and-so” (Sotah, chapter 1, law 1).
Proof for the first interpretation may be brought from the language of Deuteronomy:
“They made Me jealous with a no-god, they angered Me with their vanities; and I will make them jealous with a no-people, I will anger them with a base nation” (32:21).
Proof for the second interpretation may be brought from the prophecy of Joel:
“Then the Lord was jealous for His land and took pity on His people” (Joel 2:18).
And Rashi explains there too, in his second interpretation, that it is a term of warning.

Jealousy as a character trait is bad (even if it has positive results, like scholars' rivalry). Jealous behavior can have its place. The ideal is to be without the trait of jealousy, but still to act jealously when one decides to.

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Why is it sometimes treated as something positive?

As I explained, I do not think there is any place where the trait of jealousy is treated as positive. Jealous behavior is sometimes treated as positive.

Can a person channel the feeling of jealousy through the intellect toward positive directions?

Definitely. For example, toward self-improvement through scholars' rivalry. Or to fight evil through zeal for God. It is still a bad trait and tendency, but these are positive ways to leverage such a trait if it exists. About this it was said, “and to serve Him with all your heart” — with both your inclinations.