The claim, that the CIA funded the Taliban in the 1980s to fight the USSR, is false. This is for the primary reason that the Taliban did not exist.

But the answer really does not end there. The United States government did fund numerous Islamist opposition groups to the communist government in Afghanistan, and did so persistently from the founding of the communist government to its downfall. This money, weapons, training and other forms of state aid for the anti-communist effort was funneled to numerous mujahadeen groupings, and pretty much anybody who said they did not like the Soviet Union or PDPA. The US was not the only one funding these groups, with the People's Republic of China also seeing the presence of another pro-Soviet government on its borders as a threat. There was also backing from numerous right wing governments in neighbouring countries (all of which would have themselves been beneficiaries of American aid, and were using that fact to offload older or surplus equipment to the mujahadeen), and from other Western states such as the United Kingdom. It is important to keep in mind that direct distribution of support was largely left to local allies, such as the Pakistani ISI.

Once communism was overthrown in Afghanistan, however, the arms and money did not vanish into thin air. The Taliban movement was formed, and it won to its cause numerous mujahadeen figures who had been trained, armed and funded by the American state. It also got arms and funding from Pakistan (again, which would have been a beneficiary of American aid) - essentially, while the US never directly backed the Taliban, it did back many of the tributaries that fed into its formation and composition. One need only take a look at its founders, Mohammed Omar and Abdul Ghani Baradar, both veteran mujahadeen fighters who served with Hezb-i Islami Khalis, which was one of the favoured groupings of the ISI (who distributed US weapons and funds). The Taliban would go on to receive direct support from Pakistan, so even if it was not US intention, they were indirectly supporting them.

At the same time, the Taliban fought against groups who were more explicitly US-backed, such as the mujahadeen organised around Ahmad Shah Massoud who would go on to form the Northern Alliance, whom the US placed in power in 2001. So rather than American-backing of the Taliban, it was the fact that the United States flooded a country loaded with political instability and civil war with weapons and other means to wage war. And some of that inevitably made its way into Taliban hands as a legacy of US involvement, and the strategies of American allies.

Edit: The response from /u/Kochevnik81 below fills out more to this which should be of interest to people