Can a Muslim woman choose not to be get married irrespective of her family's stances? I mean is it sinful for her if she wishes to remain unmarried?
The guidance of Islam is to get married:
وَمِنْ آيَاتِهِ أَنْ خَلَقَ لَكُم مِّنْ أَنفُسِكُمْ أَزْوَاجًا لِّتَسْكُنُوا إِلَيْهَا وَجَعَلَ بَيْنَكُم مَّوَدَّةً وَرَحْمَةً ۚ إِنَّ فِي ذَٰلِكَ لَآيَاتٍ لِّقَوْمٍ يَتَفَكَّرُونَ
And of His signs is that He created for you from yourselves mates that you may find tranquility in them; and He placed between you affection and mercy. Indeed in that are signs for a people who give thought.
It is clear from the verse above that the drivers are tranquility, affection, and mercy; in addition to establishing a family. The verse applies to both men and women alike. The Prophet ﷺ got married, and explicitly expressed that this was his guidance (See Sahih Muslim » The Book of Marriage » Hadith 1401).
In Al-Mughni (Arabic: المغني) by Ibn Qudamah (Arabic: موفق الدين عبد الله بن أحمد بن قدامة), this specific question is addressed. It is basically left to the individual to decide, man or woman alike, based on their knowledge of their own conditions:
- For those who have desire and are capable of marriage (physically, mentally, and financially), it is wajib (obligatory: rewarded when done,and punished when not done) to get married. Ahmad ibn Hanbal said that staying single is not from Islam, unless justified.
- For those who have desire but are not able to get married (for valid reasons related to oneself or one's family), then it is mustahab (preferred: rewarded when done, but not punished when not done) to get married. If one cannot get married, then one should revert to extra fasting as a deterrent from falling into sins (see Sahih Al-Bukhari » Book of Fasting » Hadith 1905)
- For those who have no desire, it is mustahab to get married if some of the objectives of the marriage can be fulfilled, but it mustahab not to get married if the marriage would deprive the partner from achieving their objectives of marrying.
منهم من يخاف على نفسه الوقوع في محظور إن ترك النكاح فهذا يجب عليه النكاح في قول عامة الفقهاء لأنه يلزمه إعفاف نفسه وصونها عن الحرام وطريقه النكاح
— NOTE: My own translation, so treat with care:
Those who fear for themselves from falling into what is forbidden if they do not get married. For those, it is mandatory to marry in the opinion of the general jurisprudence scholars, as this protects them from sinning and provides a legitimate means [to fulfill their desires] through marriage.
من يستحب له وهو من له شهوة يأمن معها الوقوع في محظور فهذا الاشتغال له به أولى من التخلي لنوافل العبادة
It is mustahab for those who have desire that they can control and guard themselves from committing what is forbidden, it is better for them occupy themselves with marriage than to dedicate more time to extra rituals of worship.
من لا شهوة له إما لأنه لم يخلق له شهوة كالعنين أو كانت له شهوة فذهبت بكبر أو مرض ونحوه ففيه وجهان: أحدهما يستحب له النكاح لعموم ما ذكرنا والثاني التخلي له أفضل لأنه لا يحصل مصالح النكاح
Those who have no desire, either because this is how they were created, or those whose desire faded due to age or illness, there are two options: The first is that it is mustahab to get married based on what was previously mentioned, but the second is that it is preferred not to get married as the objectives of marriage will not be fulfilled.
For more information, you may refer to Islam Q&A 112000 (Arabic only).