It is permissible to marry off a minor without her consent because her intellect is underdeveloped and she does not truly understand what is good for her or bad for her. For example if a minor needs medical treatment you will administer it regardless of her consent, you won't ask her whether she permits it or not. Similarly you will admit her to a school, manage her finances, forbid her from doing dangerous things etc. even though she dislikes it. Her consent is immaterial because she does not have the mental ability to decide what is best for her. Rather the parent is responsible for deciding that. And it is possible that a parent finds a very good match for marriage which would be lost if he waits for the daughter to first reach adulthood.
There is no consensus on marring off an adult, sane, free virgin without her consent. For example the Hanafis do not allow it, and this stance is shared by other individual scholars such as various hadith scholars, Al-Awzaa’i, al-Thawri, Ibn Hazm, Ibn Taymiyyah etc. However most of the other madhabs do allow it.
Their reasoning is based on the hadith:
الثيب أحق بنفسها من وليها والبكر تستأمر وإذنها سكوتها
The previously-married woman has more right concerning herself than her guardian does, and the virgin should be consulted, and her permission is her silence.
— Muslim
As this hadith says that only a non-virgin has more right over herself than her guardian, which implies that a virgin does not have this right. Rather it implies that a virgin's guardian has greater right over her. And this right of the guardian is understood to mean the option of marriage without her consent. Further it is understood that consulting (asking the permission) of a virgin is recommended but not obligatory and that her say on the matter is not binding.
As for ahadith which seem to oppose this madhab, they are explained in one of the following ways:
Some of those ahadith have disputed authenticity or there is a dispute on their wording.
The ahadith on cancellation of such marriages are understood to be talking about adult, non-virgins. Not about virgins or minors. In some ahadith this is explicitly mentioned:
عن خنساء بنت خذام الأنصارية، أن أباها، زوجها وهى ثيب، فكرهت ذلك فأتت رسول الله صلى الله عليه وسلم فرد نكاحه
Khansa bint Khidam Al-Ansariya:
That her father gave her in marriage when she was a matron (i.e. divorced or widowed) and she disliked that marriage. So she went to Allah's Messenger (ﷺ) and he declared that marriage invalid.
— Bukhari
In the ahadith on cancellation of such a marriage, It is possible that the marriage did not fulfill the conditions that are necessary for a such a marriage. For example the status difference between the bride and groom, or some other defect in the groom.
إن أبي زوجني ابن أخيه ليرفع بي خسيسته
My father married me to his brother's son so that he might raise his status thereby.
— Ibn Majah
The ahadith on seeking consent are implicitly understood to be about marriage of orphans which is done by guardians other than their biological fathers. The ruling on that is different from that of marriages arranged by the father of the bride.
تستأمر اليتيمة في نفسها فإن سكتت فهو إذنها وإن أبت فلا جواز عليها
An orphan girl should be consulted with regard to marriage, and if she remains silent, that is her permission. If she refuses then she is not to be forced.
— Nasai
The ahadith on seeking consent are interpreted to be a recommendation and not an obligation. And the result of that consultation is not considered binding.
Note however that marrying off a virgin or minor without her consent has conditions, and is discouraged unless it serves a valid interest.
Ref:
فلما قسم النساء قسمين، وأثبت الحق لأحدهما، دل على نفيه عن الآخر، وهي البكر، فيكون وليها أحق منها بها، ودل الحديث على أن الاستئمار هنا، والاستئذان في حديثهم؛ مستحب غير واجب.
— al-Mughni
البكر البالغة العاقلة: تثبت عليها عند الجمهور غير الحنفية ولاية الإجبار
— Fiqh al-Islami wa Adillatuhu
