The Havi(oblation) that is poured in fire during a fire sacrifice(Yajna) is the only food for the Gods.Without getting Havi from Yajna the Gods gradually become weak.
Now,the Gods are the positive forces of nature that sustains life and sustains the entire universe.
So, maintaining their vigor and power is of utmost importance and is in good interest of every creature that inhabits this creation.
So, Yajna or Puja to Gods take a supremely important position for a smoothly functional universe.
That's also the reason you often find that the Asuras(representing the negative forces of nature who are constantly in war with the Gods) are always very eager to disrupt Yajnas and Pujas. By doing that,they just want to get the Gods weak that's all.
Now ,the Brahmins ,who are well versed in the Vedas and other scriptures are the only ones capable of performing these religious duties(like Yajna etc) perfectly.
So,their life becomes understandably far more important than those of some other (Non-Brahmin)human beings.
There is also a similar differentiation done between Cows and other animals.
You will find scriptures saying that killing Cows is one of the most grave sins possible.
But killing some other animals for example is not that much of a big sin.
Now, that might sound rationally wrong to few.
But,the reason again ,for such importance of cows, lies in Yajnas.
The Havi that is poured in Yajna is mostly Ghee which can only be obtained from Cows.
So,Cows form the very root of fire sacrifice.
Thus, Cows take a supremely important position among all animals just like the Brahmins who take a similarly important position among human beings.
A smoothly functional universe is impossible without the Gods who are in turn fully dependent on Yajnas for sustaining their strength.And ,Yajnas again are impossible to perform without either the Brahmins or the Cows being present.
That is why killing a Brahmin or a Cow both come under the worst possible sins.
Adding a scriptural source (courtesy Keshav Srinivasan) which aptly describes the importance of Yajna in Dharma:From this page:
havisham parinamo'yam yat etad akhilam jagat
Meaning-This whole universe is the result Or transmutation of