Question

Why is it difficult to convert miles to yards

Answer 1

There's really no "why", because it's not difficult at all.
 
Simply multiply the number of miles by 1,760, and bada boom,
there you have the same distance described in yards.

Answer 2

In today's technological age it would be immensely easy to make such a conversion. There are countless tools on the internet that can do the job for you incredibly quickly and easily. Nevertheless, I'll give you an idea about how it could be done.

$1\quad mile\quad =\quad 1760\quad yards\\ \\ \frac { 1 }{ 1760 } \quad \times \quad 1\quad mile\quad =\quad 1760\quad \times \quad \frac { 1 }{ 1760 } \quad yards\\ \\ \frac { 1 }{ 1760 } \quad miles\quad =\quad 1\quad yard$