Step 1: Define the condition.
Tinea capitis is a dermatophyte infection of the scalp and hair shafts. Because the fungus invades the hair follicle and shaft, topical agents cannot penetrate adequately.
Step 2: Choose the treatment.
The treatment of choice is systemic (oral) antifungals - classically griseofulvin, and increasingly terbinafine or itraconazole. Oral therapy reaches the hair follicle and eradicates the infection, which topical antifungals alone cannot achieve.
Step 3: Why the other options are wrong.
Antibiotics treat bacterial infection and have no role unless there is secondary bacterial superinfection (e.g., kerion). Methotrexate is an immunosuppressant for inflammatory/proliferative disorders such as psoriasis - it would worsen a fungal infection. Topical steroids suppress inflammation but promote fungal spread (tinea incognito) and never cure tinea capitis.
Key fact: Tinea capitis requires oral antifungals because topical drugs cannot penetrate the infected hair shaft.