Why do we show homologous chromosome

Here's a site that shows meiosis and mitosis side by side (you have to advance through the pages to see each step). This should help you understand the similarities and differences between the two process (remember, in meiosis, cells undergo two divisions resulting in 4 haploid daughter cells; in mitosis, there is only one cell division resulting in 2 diploid daughter cells).

http://www.pbs.org/wgbh/nova/miracle/divi_text.html

 

I'm not sure what you're trying to ask then. The pairing up of homologous chromosomes is the major difference between meiosis and mitosis, so if you're not sure why that's happening, then you aren't understanding the difference between the two processes. In meiosis I, homologous chromosomes pair up, and in mitosis they do not. It is because the homologous chromosomes separate to two different cells during meiosis I that you have haploid cells by the end of meiosis I (and then in meiosis II the sister chromatids separate to separate cells). In mitosis, the homologous chromosomes don't pair up, so one sister chromatid of EACH chromosome goes to each new cell formed, which means you still have a diploid cell.

 

Perhaps this will help:

During mitosis only chromatids separate

During meiosis (1) first homologous pairs of "chromosomes" separate (Meiosis I)
then, (2) chromatids separate (Meiosis II)

Now, because chromatids separate in both mitosis and meiosis, the primary difference in the two processes "is" the formation of homologous pairs.

More to detail. You need the homologous pair separation step to end up with haploid number of chromosomes in gametes. The separation of homologous pairs means that each gamete will receive one chromosome from every homologous pair. This is called Mendel's Law of Segregation. In this way, it is then possible for a tall individual to pass on a gene for shortness to offspring.

As stated by all of the previous posts, you really do need to understand the homologous pair concept to grasp the fundamental difference between mitosis and meiosis.