Why did Cowboys have to take the cattle east?

Because all the cattle that had been raised back east were all killed due to meat needed for the Civil War soldiers. Meat (in the form of beef) came into high demand, so men set out west to find the cattle that were supposedly roaming the south-western part of the US. Upon finding them, they rounded them up in herds up to and over a thousand head and trailed them back east. This turned into a profit-making venture, which attracted more men to ride the range and herd cattle to markets back east.