The premise of "issuing bonds at parity, yield to maturity = coupon rate" is that the discount rate of bonds is the same as that of coupon rate. If the interest is paid in installments, it will only be equal if it is converted into cash by compound interest.

If coupon rate only pays interest and simple interest (repayment of principal and interest at maturity) and yield to maturity only pays interest and simple interest, the bonds issued at parity are coupon rate = yield to maturity. If simple interest is discounted by compound interest, it is impossible to calculate the equality between the two.

See if the topic mentions simple interest discount.

I hope it helps.