This wrong:
<div class="person__arm">
<div class="person__arm--left"> ... </div>
<div class="person__arm--right"> ... </div>
</div>
There are three elements!
Element with modificator should write so:
<div class="person__arm person__arm--left"> ... </div>
<div class="person__arm person__arm--right"> ... </div>
And you can use binary notation with modifiers (person__arm_left), or use "type", for example:
.person__arm_type_left {}
.person__arm_size_big {}
.person__arm_theme_main {}