On top of military and strategic reasons, here are a few non-military angles that gives India a reason to launch a missile towards Pakistan.
Escalation against Pakistan/China will bring India-USA back together
India has refused to take a position against Russia on Ukraine and USA is offended for India not proving an ally at the time of need. They are also considering sanctions against India under CAATSA for procuring Russian S-400 and for India canceling HQ-9 orders from the USA. It's likely that USA will take some action against India.
However, an escalation against China or Pakistan will immediately invoke doctrine of necessity in Washington and they'd be willing to overlook India in wake of wider strategic objectives. Thus India-and-USA could come together if the situation escalates and India may be looking to do exactly that.
Sabotaging OIC summit in Islamabad
Timing of this incident is important as Pakistan is about to host OIC conference on 23rd March 2022. This conference will elevate dispute of Kashmir and support towards minorities and Muslims in India. If Pakistan would respond to a missile strike, it will have to postpone this incident and may loss opportunity to host it altogether - a win from Indian stand point.
Poke Pakistan at a time when it is unlikely to respond
India knows that under current political and international situation (OIC summit, Australia touring Pakistan and no-trust motion against PM), its in Pakistan best interest to let go a response. This will give Indian Government a chest thumping opportunity to warmup its political mass and benefit Nirandra Modi one more time.