Why do we use I and Q signal instead of the original signal

Do you know the math behind this idea ? I mean why an oscillator has been used to drive two mixers by 90 degree phase difference ??
It's a homework for you..

There are many reasons for using the I and Q channels.
To mention just one, it comes down to signal processing theory.
In other words, it has to do with the composition of the signal.
Currently, signals with I and Q structure are used for communication.
To demodulate this signal, a demodulator with I, Q structure must be used.

The short answer is that you could if you had an RF sampling ADC and implement the mixers in digital. But you would still need the mixers.

In a system like this, I and Q channels are orthogonal to each other (they can't be represented as each other, they complete the I/Q plane). Think of mixer as multiplication, and let's say you only mix with 0 degree phase. This would multiply the information carried orthogonal to the mixing signal with 0 so you'd lose the Q channel information (Although technically you can do some non-linear stuff to mix them both but that's not the point). You can find the proof in most textbooks, or do it yourself using trig identities.

Very simple explanation is, assume Q is information carried by a sin wave and info is not time varying, I is information carried by a cos wave and info is not time varying. If you multiply a sin with a sin at the same frequency/phase, you'd get a number, but if you multiply sin with a 90deg phase shifted sin (or in other words a cos wave which is our Q channel), you'd get 0. So you need two phases to cover all the information in I/Q plane.

Disclaimer: This is a very simple explanation. There is more to it, I'm just trying to give context.