Why are two registers with the same value not equal?

Question

.section .note.GNU-stack,"",%progbits
.text
    .global binary_search

binary_search:
    push %rbp;          // move rbp to stack
    mov %rsp, %rbp;         // move rsp to rbp
    mov %rdi, %rax;         // move head
    mov %rsi, %rcx;             //move len
    
    mov %rcx, %r12;
    dec %rcx;
    
    mov %rdx, %r9;              //move target
    mov %rcx, %r10;         //mid=right
    
    mov $0, %r8;            //left = %r8, %rcx = right, %r10 = mid
    
loop:

    cmp %rcx, %r8;          //if left > right, -1
    jg final;

    mov %r10, %rcx;         //mid=right 
    sub %r8, %r10;          //mid=right-left
    sar $1, %r10;           //mid/2
    add %r8, %r10;          //mid+left

    mov (%rax, %r10, 4), %rdx;
    cmp %r9, %rdx;
    jne check;
    je ret_mid;
    jb inc_left;

    dec %r10;
    mov %r10, %rcx;
    
    jmp loop;

check:
    mov $10, %rax;      // set curr->next = prev
    pop %rbp;
    ret;
inc_left:
    inc %r10;
    mov %r10, %r8;
    jmp loop;
    
ret_mid:
    mov %r10, %rax;         // set curr->next = prev
    pop %rbp;
    ret;
final:
    mov $-1,%rax;
    pop %rbp;
    ret;
    

I've been testing this binary search algo with the array (0,1,2,3,4). he arguments I gave it were that array, 5, 2. I checked that (%rax, %r10, 4) is also 2, but why is that and %r9 not equal? It never goes to ret_mid. I don't understand why they are not equal even though the value in both is 2.