Born Qvist (his mother's name), Rovsing, in Copenhagen, was adopted in 1889. From the death of his father in 1910, he lived the life of a wealthy gentleman of independent means. Except for a high-school diploma, he received no formal education.
Tennis was his primary and all-consuming interest. He won several Danish championships in doubles, and was a Swedish and Norwegian International Champion in 1916 (men's single). In 1923 he reached the finals (doubles) at the Indoor World Championship in Barcelona. He was considered to have a strong serve and a good drive.
In the upper-class world of Tennis, Rovsing's openness as a homosexual seems not to have caused problems. However, tennis tournaments were organised by and played in clubs that were prinarily football (soccer) clubs. Consequently the Danish Lawn Tennis Association was a subdivision of the Danish Football Association.
When in 1917, the details of a visit to Rovsing's home by a young tennis player were reported to the Board of Directors of his tennis and football club, Rovsing was confronetd with the working-class respectability of organised football. He argued that neer committed a criminal act, but he was nevertheless excluded from all clubs and tournaments under the Danish Football Association.
The exclusion was revoked in 1921. This caused opposition from the Copenhagen Football Association and in 1924 Rowsing was once more excluded from participating in tournaments in Denmark. His "opinions and his conduct" precluded him "from participating in tournaments with related access in the showers and locker rooms of young players".
In 1927 Rovsing himself financed and made preparations for a separated tournament. Most of the prominent tennis players agreed to participate. The Lawn Tennis Association, however, declared that Rovsing could not participate. He now sued the Danish Football Association. The outcme was a foregone conclusion. The High Court upheld the exclusion from tournaments as justified by Rovsing's sexual conduct and by the duty of the Danish Football Association to protect his young members.
In Hellerup, a suburb in northern Copehagen, Rovsing in 1919 built himself a house and a magnificent wooden tennis hall which became the home of his own tennis club, the Dansk Tennis Club. It neither was nor is affiliated with the Danish Lawn Tennis association. It is partly financed through a foundation created by Rovsing in his will.
Rovsing travelled in the Far East and lived for a long period in Bali. In a book he gave a first hand account of the delights of Balinese youths as opposed to the drab and restricting conditions in Denmark.
In the 1950s he became a prolific contributor of articles to the homophile journal, Vennen (The Friend), which he briefly supported financially. In 1955 his home was ransacked by the police, and he was arrested and held in custody for 15 days charged with having had sex with a minor, a prostitute under the age of 18. He denied the charges, which he saw as a revenge for his writings, but was given a suspended sentence of 30 days in jail for indecency.