Is it permissible for me to travel to learn sewing at a distance exceeding one hundred kilometers without a mahram, knowing that my family refuses to accompany me and justifies this by saying that transportation is safe and that this is not travel like in the days of the Messenger, may Allah’s peace and blessings be upon him?

It is not permissible for a woman to travel without a mahram (definition), according to the majority of scholars, except in cases of dire necessity. If a mahram is not available and the woman needs to learn sewing in a distant place, and she is unable to learn it locally, then she may follow the opinion of those who permit a woman's travel without a mahram when there is no fear of fitna, especially if accompanied by other women. She must avoid everything that could cause fitna. If traveling without a mahram leads to fitna or falling into something forbidden, then it is not permissible.