Not every hesitation is the kind of modesty praised in religion. Avoiding a truthful statement, failing to ask an essential religious question, refusing to help someone wronged, or concealing one's own mistake may arise from fear rather than virtuous haya.
Examples:
A student has an easy chance to cheat but refrains out of awareness of Allah — an appropriate expression of modesty.
A student does not understand a lesson and asks respectfully — a legitimate act of seeking knowledge.
Someone's silence would leave another person exposed to wrongdoing — appropriately intervening can be a moral duty.
In مِنَ الْإِيمَانِ, مِنْ means 'of / from among' and الْإِيمَانِ is 'faith.' The central predicate is شُعْبَةٌ, while the following phrase identifies what the branch belongs to.