As the other answers here describe, the Fugitive Slave Law of 1850 meant that there was nowhere safe for an escaped slave anywhere in the United States. That is why Harriet Tubman had to take her runaway slaves all the way to St. Catherines in Canada.

Slavery was legally abolished in Canada in 1834. At the time, Canada was still part of the British colonies. Although they were major players in the slave trade in the previous century, abolitionist sentiments became the norm in Britain by the early 1800s. They abolished the slave trade in 1807 and outlawed slavery throughout its entire dominion in 1833 (the law went into effect the following year).

When this happened, Canada became a safe refuge for escaped slaves. However, before the passage of the Fugitive Slave Law, most escaped slaves were content to find a new home in the northern states of the United States. After 1850, many were compelled to head further north to Canada. Situated just over the Niagra River in Ontario, St. Catherines soon became Harriet Tubman's destination. There was a relatively welcoming community of people opposed to slavery there.

In fact, St. Catherines had been a destination for escaped slaves long before Harriet Tubman. The Act to Limit Slavery in Upper Canada of 1793 outlawed the importation of slaves to the territory. It did not free existing Canadian slaves, but it meant new arrivals could not be enslaved. As early as the 1820s, St. Catherines' location near the US border made it an attractive destination for fugitive slaves. When slavery was finally abolished in all of Canada in 1834, a thriving black community developed in this town. This made it even more attractive to Harriet Tubman and other conductors on the Underground Railroad.

The Fugitive Slave Law of 1850 tightened rules against escaped slaves and made is so that everyone had to help U.S. Marshals return slaves to their owners. The courts also awarded slave catchers more for guilty verdicts than they did for declaring someone free; therefore, there was more incentive to catch a black person and sell him South than there was to leave him alone. The law also made it a crime to help escaped slaves. This law went against many personal liberty laws passed at the state level that previously allowed many Underground Railroad conductors to legally operate. Though Albany was a free state and New York supported the ardent abolitionist William Seward, Tubman knew that escaped slaves would not be truly safe there. Many places in the North were also hesitant to employ black people.

By going to St. Catherine's in Canada, Tubman took the escaped slaves to land that was truly free. Britain abolished slavery in 1833. Many abolitionists lived in the city and they were willing to help escaped slaves start new lives in Canada. Though some slave owners protested against Canadian abolitionists helping slaves escape North, no one dared impede on British sovereignty by invading Canada in order to take back their property. Canada also treated the escaped slaves more favorably than they would be treated in many Northern cities.

In the 1850s, the Fugitive Slave law was in effect. This made it legal for enslaved people who had fled to the northern, non-slave states such as New York to be recaptured and returned to their "owners" in the southern (slave) states. The Dred Scott decision confirmed the notion that an escaped slave could not be free simply by virtue of being on free-state ground.

The Fugitive Slave Law represented an enormous extension of federal power in favor of the slavery oligarchy of the South. It is the ultimate irony that the South would later claim that the Civil War was fought to defend "state's rights" in the abstract against the encroachment of federal power, when the slaveholders had been all to eager in the case of the Fugitive Slave Law to use federal law to protect the institution of slavery. So, Tubman and others who facilitated the escape of enslaved people realized that those people would only secure their freedom if they were escorted across the northern border into Canada or somewhere else outside the U.S.

There were a few reasons why Harriet Tubman escorted her escaped slaves to St. Catharines, Ontario instead of stopping in Albany, New York. One reason was that the Fugitive Slave Law that was part of the Compromise of 1850 changed everything. Prior to the passage of this law, a slave that escaped to the North, by crossing the Mason-Dixon Line, was generally safe. The likelihood of being captured and returned to the South was very, very low. However, when the Fugitive Slave Law was passed, Northerners were required by law to help capture runaway slaves. As a result, it was no longer certain that reaching the North would ensure freedom for the runaway slaves. The only way to ensure freedom was to escape to Canada.

St. Catharines was a town in Canada that was friendly to African-Americans. There were many abolitionists who lived here. Slaves who got to St. Catharines were safe from recapture and from being returned to their owners. As a result, in order to ensure the safety of the runaway slaves, Harriet Tubman had to get the runaway slaves to Canada.