Reference-work discussions of the asymmetry between 'benign' and 'malignant'
H. W. Fowler, A Dictionary of Modern English Usage, first edition (1926) seems to share your view as to the lack of symmetry in such usage:
benign, benignant, malign, malignant. The distinction between the long & short forms is not very clear, nor is it consistently observed. But it may be said generally that benign & malign refer rather to effect, & benignant & malignant to intention or disposition : [examples omitted]. ... The difference is the same in kind, though less in degree, as that between beneficent, maleficent, & benevolent, malevolent. It is to be noticed, however, (1) that the impulse of personification often substitutes the -ant forms for the others, e.g. as epithets of destiny, chance, &c. ; (2) that the distinction is less generally maintained between benign & benignant than between the other two (e.g., of benign appearance is common, where benignant would be better) ; (3) that nevertheless in medical use as epithets of diseases, morbid growths, &c., the forms are benign (as would be expected) & malignant (contrary to the rule) ; this use of malignant is perhaps a stereotyped example of the personifying tendency, which benign escaped because benignant, a recent formation, did not exist when the words were acquiring their medical sense.
William Haubrich, Medical Meanings: A Glossary of Word Origins (2003), in an entry for malignant, shows an unfortunate lack of interest in the order of occurrence of benign, malign, benignant, and malignant in English:
In English there are, among others, two pairs of nearly equivalent words: “benign/benignant” and “malign/malignant.” Curiously, in medicine (and more particularly in pathology) we have chosen to use the shorter of the former pair and the longer of the latter pair to contrast the behavior of certain diseases, especially neoplasia. We speak or write of "benign" (rather than "benignant") tumors in contrast to "malignant" (rather than "malign") tumors. The choice is little more than a matter of custom.
Dwight Bolinger, Language — The Loaded Weapon: The Use and Abuse of Language Today (1980) takes a very different tack, however, arguing that the decision to match benign with malignant in medical usage was calculated to serve the practical purpose of distinguishing more clearly between the two words:
Tumors are not malign and benign, or malignant and benignant, with the same ending in both, as would seem logical. Instead, a physician calls one benign and the other malignant — and is less likely to be misunderstood.
Bolinger's argument is not irrational, by any means, but it doesn't address the chronology of the word choices any more than Haubrich's discussion does.
Evidence for Fowler's dates-of-origin theory
Merriam-Webster's Eleventh Collegiate Dictionary (2003) dates the four words (as adjectives) as follows: benign, 14c; malign, 14c; malignant, ca. 1545; benignant, ca. 1782.
A Google Books search turns up numerous instances of benignant from before 1782, the earliest of these being from The Museum, Or, The Literary and Historical Register, volume 2 (1746) [combined snippets; date not independently confirmed]:
Is the Mind distemper'd and dissonant to Society? 'Tis here the Rebel to his Maker chooses to growl at Heaven, and gratify the refining Anguish of his envious Soul, to behold it's benignant Dew cherishing the Earth.
Other early instances of benignant (with confirmed dates) appear in a poem published in The Monthly Review (February 1750):
When day declines, and evening cool/ Begins her gentle silent rule,/ Again, as fancy points the way,/ Benignant leader, let me stray:
and in another poem published in The Monthly Review (September 1750):
The sceptre's mine the monarch bears,/ I give his crown the beams it wears,/ And the rich lux'ries of his land/ Are show'rd from my benignant hand.
But despite pushing the earliest print appearances of benignant back to 1846–1850, these instances come too late to offer support to benignant as the counterpart of malignant in medicine at the time when people in the profession seem to have settled on malignant and benign.
Stephen Blancard, The Physical Dictionary (1702) includes two relevant entries:
Benignus Morbus, a favourable Disease, is that which has no dreadful Symptoms, but such as are consonant of its nature.
Malignus Morbus, a malignant Disease, is that which rages more vehemently, and continues longer than its nature seems to pretend to, as a Pestilent Fever, &c.
The latter entry specifically refers to "malignant Disease" at a date before benignant is recorded in English. Meanwhile, Blancard uses the word benign once in his dictionary, in the entry for Laxantia:
Laxantia , Loosening Medicines , are those which with their benign particles softning and scouring the Intestines , cleanse them of their Excrements.
John Kersey, Dictionarium Anglo-Britannicum: or, a General English Dictionary, second edition (1708) indicates that benignus morbus and malignus morbus had become standardized, respectively, as benign disease and malignant disease in English medical terminology by that date:
Benign Disease, is a favourable one, that has no irregular, or dreadful Symptoms.
Malignant Disease, is that which rages more vehemently, and continues longer than its Nature seems to incline.
English doctors in the early 1700s were familiar with the terms benignus mordus and malignus mordus as indicating a disease that was normal or mild (on the one hand) or unusually virulent or severe (on the other). Why they chose to refer to the latter as malignant disease rather than as malign disease is unclear, since both adjectives were well established in English long before the beginning of the eighteenth century.
But the choice of benign disease as the counterpart to malignant disease was surely no choice at all, since benignant did not exist in English at the date when benign came into use in medical contexts. The reason for the lack of symmetry between benign and malignant in medical terminology may therefore be due in part (as Fowler surmised) to the relative newness of the word benignant in English and in part to what Fowler calls "the personifying tendency" of the -ant forms of adjectives.