When the compulsion idiom “infinitive + होना” is used with ही, it can refer to something that is “bound to happen”, i.e., something that is very likely to happen.
जब दो दुश्मन एक घर में रहते हैं, झगड़ा तो होना ही है – “When two enemies live in one house, a fight is bound to happen!”
वह रात भर जागा हुआ रहा. उसे तो सोना ही था – “He stayed awake all night. He was bound to sleep.”