In rest of the signs, at least one of the two parameters of sign and planet is common. But rulership of Scorpio by Mars is a total mismatch. Historically the concepts of rulership had evolved in Vedic astrology.
Initially the rulers of 12 zodiac signs were considered either Sun or Moon. The first decision was Cancer is ruled by Moon and Leo is ruled by Sun.
The 5 signs in anticlockwise direction in the zodiac from Aquarius to Gemini were considered to be ruled by Moon. The remaining 5 signs from Virgo to Capricorn in the anticlockwise direction were considered to be ruled by Sun. Later on as the sages understood more about the nature of other planets and their influence, they had formalized the scheme as given in the beginning where all the other planets ruled 2 zodiac signs each.
The 8th zodiac sign Scorpio is considered the most mysterious of all the zodiac signs and its ruler was decided to be Mars. Scorpio signifies action, the eternal struggle between light and darkness, the attribute of Mars but these actions are all internal and they do not manifest externally. They realized that Mars do not fully reflect or explain the mysteries of Scorpio, so they considered Ketu to be the lord of Scorpio based on its mystical and secretive actions.
Once they decided Ketu as the lord of Scorpio, they had to make Rahu as the lord of Taurus, which is opposite to Scorpio 180 degrees apart in the Zodiac because by definition, Rahu and Ketu must always be 180 degrees apart in the Zodiac. Apart from ownership of signs, the ancient sages observed that individual planets not necessarily behave in their most natural and positive way in the sign they own, but still for each planet there is one sign in which their positive qualities manifest the best, and the sign opposite to it that is 180 degrees apart in the zodiac, if the particular planet is located there, they manifest their negative qualities in the worst possible manner in that particular sign.
This they refer to as the sign of Exaltation (the best position) and the sign of Debilitation (the worst position) for the particular planet. This sign of exaltation may or may not be the sign they rule.
A more correct description will be that in sign of exaltation the planet manifests its influence in the most harmonious or balanced way and in the sign of debilitation the planet manifests in the most unbalanced way.
This scheme of exaltation and debilitation for each planet is as follows.
Sun: Aries (exaltation) and Libra (debilitation)
Moon: Taurus (exaltation) and Scorpio (debilitation)
Mars: Capricorn (exaltation) and Cancer (debilitation)
Mercury: Virgo (exaltation) and Pisces (debilitation)
Jupiter: Cancer (exaltation) and Capricorn (debilitation)
Venus: Pisces (exaltation) and Virgo (debilitation)
Saturn: Libra (exaltation) and Aries (debilitation)
Rahu: Taurus/Gemini/Virgo (exaltation). Astrologers have difference of opinion. Scorpio/Sagittarius/Pisces (debilitation)
Ketu: Scorpio/ Pisces (exaltation) Taurus/Virgo (debilitation).
Let us analyze the rational behind it again on the basis of planet/Sign type and element.