The mistake
The commonest error is reading only the birth-year animal. Your zodiac animal is just one of eight characters — the Year Branch. Two people born in the same animal year can have completely opposite charts once the month, day and hour are added.
What the classics actually say
The single most important character is the Day Master — the Heavenly Stem of your day of birth. It represents you. Every other element is read as a relationship to it: what it produces, what it controls, what controls it, what drains it, and what it competes with.
Getting it right
Reading a chart begins with judging whether the Day Master is strong or weak relative to the season and the surrounding elements. A strong Day Master wants outlets — elements it produces or controls; a weak one wants support — elements that produce or reinforce it. This balance names your favourable element.
Try it yourself: BaZi (Four Pillars) is free on FengSpark, computed to the letter.