ANSWER:
What he has said is wrong. No problem in having double intention except for fasting the 6 days of shawwal as long as one is mandatory and the other is voluntary.
http://localhost/assimnet2018/11/24/if-i-choose-to-fast-the-sunnah-of-monday-thursday-can-this-count-as-making-up-the-missed-fasts-during-ramadan-or-do-i-have-to-have-separate-intentions-for-one-fast/