Chinese is about as different from English as you can get. And one of the things that English speakers find alien and difficult about it is the tones.
Not that tones are unusual, globally speaking. According to the Wikipedia article, Tone (Linguistics):
Tonal languages are common in East and Southeast Asia, the Pacific, Africa, and the Americas; as many as seventy percent of world languages may be tonal.
However, all languages have intonation. The presenter of YoYo Chinese, Yangyang Cheng, uses this (without actually making the distinction) as a way of making tones seem more familiar, in one of her excellent videos on tones: link to it here.
When I was a teacher of classical guitar, I encountered a number of people who claimed to be 'tone deaf'. Now while this condition does exist, it is actually quite rare. What these people more often suffer from is a lack of musical training or singing experience. And by way of evidence of this, I would cite, long before I took up the study of Chinese, the ability of all Chinese speakers to handle the required tones. I have never heard of any Chinese person unable to speak their own language on account of being 'tone-deaf'. So while most abilities tend to involve some combination of nature and nurture, the ability to master Chinese tones lies firmly in the nurture camp.
I have come across the occasional Chinese-made-easy book that plays down the importance of tones, even to the extent of not bothering with them at all. (I'm not going to cite them.) This is a mistake. It is hard enough getting Chinese speakers to understand or even pay proper attention to our stumbling attempts to speak their language; they're not expecting it, and the default assumption is that English speakers are not really up to it. There's a credibility barrier to jump. To overcome that barrier, we have to speak as authentically as possible, which absolutely means getting the tones right.
If you don't know the tone, you don't know the word. The tone must be assimilated along with the syllable itself (and ideally the written character too), rather in the way that a gender must be learned along with a new word in a Romance language such as French.
I am a native English speaker, having a lot of fun learning Chinese. I think (and hope) I have a certain knack for understanding what the language is about, so that I might be able to offer something your usual Chinese class does not.