The Caldari titan being shot down is an example of Federation savagery?
Right, because we were totally shooting it down so we could glass tens of billions of people. That titan was definitely there for entirely peaceful reasons that had nothing to do with attempting the largest mass killing in history.

If someone comes into your home and threatens to shoot half your family, if you had a gun, would you not take action to prevent them from doing so?
That even the Caldari titan pilot, often known as Heth's attack dog, recognised the monstrosity of what the State was ordering speaks volumes about who was being 'savage'.

And no, war was not initially declared over "a few deep space installations".

The Gallenteans, ecstatic that there was other human life in their star system, sent uplift teams to bring Caldari technology up to speed - their world was behind in technological progress. Having done this they made mutual agreements of trade, trust, transparency, etc.
The newly formed Federation grew. Other groups were found, and more joined the increasingly prosperous Federation.

One day, an explorer suddenly came across a highly developed but previously unknown system. On further investigation, it transpired that the Caldari, alone amongst all the groups in the Federation, had built vast fleets and colonies in secret.

When confronted and asked why they'd done this, the Caldari stated that it was their own business and seceded from the Federation.
That was enough to skyrocket tensions.

And then, the Caldari razed a city.
Every man, woman and child in Nouvelle Rouvenor was killed - there were no survivors.

Is it so unreasonable that the Federation did something?
If someone was in your house and killing your family, if you had a gun to hand, would you not shoot them?
Such savagery! How could you be so vicious as to act to protect your people?