What is the importance of family in Islam? I mean by the “family” parents and children. Here in the West, a lot of people do not care for forming their own families and live their lives the way they like. Some may die without getting married or having children despite having a lot of relationships with girls.

Alhamdu-li-llah wa as-Salatu wa as-Salamu ‘ala Rasool-il-llah,
Marriage is the way of Allah’s messengers, including their last and greatest, our most beloved, Prophet Muhammad PBUH.
He commanded us to do so as he said,
“يا معشر الشباب من استطاع منكم الباءة فليتزوج، فإنه أغض للبصر، وأحفظ للفرج، ومن لم يستطع فعليه بالصوم، فإنه له وجاء.”
“O young people, let those of you who afford marriage get married for it will help them lower their gaze and protect their chastity. And for those who don’t afford it , they may fast for it will curb the sexual desire.”
He also said,
“من رزقه الله امرأة صالحة ؛ فقد أعانه على شطر دينه، فليتق الله في الشطر الباقي.”
“He whom Allah provides with a righteous woman was helped on half of his deen, so let him fear Allah regarding the other half.”
That alludes to the concept of the family being the smallest unit in the building of the community. Each one of the two spouses is half of that unit, and when they are paired/ coupled, which is the meaning of the word “zawaj”, they make a full unit.
Given all that, the destruction of that family unit is the priority of Iblees (satan), as clarified by the following hadeeth, in which the Prophet PBUH said,
” إذا أصبح إبليس بث جنوده فيقول من أضل اليوم مسلما ألبسته التاج قال فيخرج هذا فيقول لم أزل به حتى طلق امرأته فيقول أوشك أن يتزوج ويجيء هذا فيقول لم أزل به حتى عق والديه فيقول أوشك أن يبر ويجيء هذا فيقول لم أزل به حتى أشرك فيقول أنت أنت ويجيء فيقول لم أزل به حتى زنى فيقول أنت أنت ويجيء هذا فيقول لم أزل به حتى قتل فيقول أنت أنت ويلبسه التاج.”
“When the devil wakes he then dispatches his soldiers and when they return to him he says to them, ‘Whoever misguided a Muslim today, I will crown him so one of them comes out and says, ‘I made him divorce his wife.’”
The other hadeeth says: “I made him mistreat his parents.” And the third one says: “I made him commit shirk.”
Dear brother, the best guidance is that of Muhammad’s PBUH who received the last message from God.
There are 100,000 children suffering in the foster care system in one country, that is the USA. Is that fair? Who is responsible for this crime against those kids who suffer constantly from their miserable reality?
There is much more data pertaining to this, and I advise you to further research the matter
Allah knows best.