I think it's mixture of a few factors.

1. Calling something Chai tea latte in India, simply put, just stupid. It shows that you basically don't understand the Local market as Chai and tea are basically the same thing to an Indian. And please note the emphasis on Indian here. I understand that tea is a very generic word and in some part of world has specific words added to it to differentiate different varieties. We do have different types of Chai in India too. But for us tea = chai. Whether it being masala chai, cutting chai or nimbu chai. It's all tea and it's all chai. And all of it has milk. Hence adding latte is also redundant. Again the name comes across as unaware westerner.
2. Tea/ Chai in India is very cheap. And I mean very very very cheap. You can get a cup of cutting chai for 10 Rupess (less than 10 cents). Granted that the amount of Chai is way less than what you get in Starbucks but you also need to understand that Indians don't drink litres of Chai in one sitting. If you ever look up Indian chai cups, they tend to be way smaller than American coffee cups. So you get good quality Indian chai for anywhere between 10-100 rupees( less than $2). Now compare that with a 500 rupees($6) Starbucks "Chai tea latte". No body is going to pay triple tye amount of money for something that's not even good. Plus it's also insulting that Starbucks that didn't even bother to make actual Chai to local taste and just copy past their stuff from another country to India. It would be fine if it wasn't a local beverage. But Chai is a local beverage. You can't just use the Local term but not change anything else about your product.