ALLAH swt says in Quran: Nisa 4:36
“And serve Allah and do not associate anything with Him and be good to the parents and to the near of kin and the orphans and the needy and the neighbor of (your) kin and the alien neighbor, and the companion in a journey and the wayfarer and those whom your right hands possess; surely Allah does not love him who is proud, boastful;”
Being good to parents means to respect them and to be kind to them, as they treated us with kindness.
In another place ALLAH swt says: Anaam 6:151
“---Be good to your parent---”
The kindness towards parents is not the ordinary kindness but it should as our parents treated us with kindness and with love. We should be grateful to ALLAH swt that HE made parents for us who love us without expecting any return and their love for us never dies even when we sometimes become bad kids.
So, we are bound to respect our parents because it is ordered to us by ALLAH swt to do so, rejecting HIS order means doing kufr.
If parents have rights they also have some obligations and farz with respect to their parenthood. Being parent is a huge responsibility because good parents make the personality of their kids good, and bad parents are equally guilty if their children are not good and threat to the society in any way. It has become a common practice to kill children and then to commit suicide which is haram and ALLAH SWT HAS forbidden it in HIS holy book Quran:
Anaam 6:151
“And do not slay your children for (fear of) poverty-- We provide for you and for them-- and do not draw nigh to indecencies, those of them which are apparent and those which are concealed, and do not kill the soul which Allah has forbidden except for the requirements of justice; this He has enjoined you with that you may understand.”
The sustainer and the provider of everything is ALLAH swt, ask Him only. To kill children out of fear of hunger is a grave sin and disbelief because it only means that the person who has decided it or had done it was hopeless from his CREATOR.
Parent child relationship has been talked about Quran in many places and whenever ALLAH swt or HIS messenger s.a.w.w talked about this relation, the meaning was to not only realize their duties towards each other but also to take care of this relation to seek ALLAH’s pleasure.