Why do we need circular convolution? I am undergoing a course on DSP and we were recently introduced to the amazing concept of DFT. 

But I have some apprehensions against it. DFT is supposed to be the methodology of fourier transform, as implemented in hardware or software. Now, if I want to convolve two signals' DFT, I could simply linearly convolve them. There would be no wraparound error, because all that I have to do to implement linear convolution is tell my computer that the array now flips and then multiplies and slides - i.e., linearly convolves. 

Circular convolution was developed to avoid wraparound error; however, the computer does not know that DTFT is a periodic function, and, thus, shifting the DFT array will render me with a circular shift. 

I know my opinion is rather radical, but I am sure that this is because I have a very abstract level acquaintance to this concept. Can someone enlighten me more, herein?
I think your confusion comes from the fact that when we talk about "circular convolution" we are not doing a convolution operation in the frequency domain.  Rather we are multiplying the two DFT arrays together, element by element.

When we switch back to the time domain via an inverse DFT, we have effectively done a circular convolution in the time domain.