Because he was the best writer on the committee.
Among those on the committee to write a draft of the Declaration were Benjamin Franklin, John Adams, and Thomas Jefferson. It was Adams who suggested that Jefferson should write the draft. Adams told Jefferson that he (Jefferson) was the best writer on the committee.
Adams also said that he (Adams) couldn’t write it because too many people in Congress didn’t like him, whereas everyone liked Jefferson. Adams was often outspoken and irascible, where Jefferson was shy and soft spoken.