The key pharmacologic principle is penetration. Tinea capitis is a dermatophytosis that lodges inside the hair follicle and shaft, a compartment topical creams cannot reach in effective concentration. Therefore cure demands a drug delivered systemically.
Oral antifungals - griseofulvin (the traditional first choice in children), terbinafine, or itraconazole - accumulate in keratin and the follicle, clearing the organism. Adjunctive antifungal shampoo reduces shedding but is never used alone.
The distractors are traps: antibiotics target bacteria (useful only for a secondarily infected kerion), methotrexate immunosuppresses and would aggravate infection, and topical steroids drive tinea incognito by masking inflammation while the fungus spreads.
\[\boxed{\text{Oral antifungals}}\]