Many formal language learning methods can be both emotionally and intellectually demanding.
The former is par for the course. It’s tough to stretch your comfort zones, interact in a new language and risk rejection without getting emotionally worked up. Being emotionally invested in language learning is, as far as current learning methods go, unavoidable. There are things you can to lessen the anxiety and negative feelings, though, from meditation to deep breathing to other types of mental health practices.
The latter, on the other hand, is only a prerequisites for some learning approaches. If you sign up for a course where grammar lessons and vocabulary exercises are the norm, then it becomes an intellectually challenge too. However, if you eschew those kinds of materials and go for less-structured methods (such as language tutoring software based on simulated immersion), you can easily remove the intellectual demands.
Some people prefer to be challenged intellectually. Others don’t. Depending on how you want to learn language, you should definitely make a choice whether you prefer one or the other. Both sides of that comparison can work, by the way, provided they are a good fit for what you’re willing to give.
Do you find grammar books especially daunting? Do you hate having to take notes, study textbooks and follow detailed instruction? Then look towards language programs that minimize intellectual demands. If, on the other hand, the intellectual aspects of learning make the emotional demands easier to meet for you, then you’re likely to benefit most from an approach based upon traditional instruction.