The Buddha taught much in regard to suffering but I think you are misinterpreting the meaning of "attachment" in relationships. In my opinion when the Buddha spoke of "attachment" he meant "clinging." Having a relationship with another is not necessarily clinging unless one is possessive--much as a compulsive person would seek ownership of another.
If something should happen to your significant other, if you should dissolve your relationship, would there be sorrow? Undoubtedly, yes but that is a part of the living cycle but not necessarily clinging.
You may wish to read the Sigalovada Sutra ( http://www.accesstoinsight.org/lib/authors/narada/wheel014.html ) in which the Buddha states:
"In five ways, young householder, should a wife as the West be ministered to by a husband:
(i) by being courteous to her,
(ii) by not despising her,
(iii) by being faithful to her,
(iv) by handing over authority to her,
(v) by providing her with adornments.
"The wife thus ministered to as the West by her husband shows her compassion to her husband in five ways:
(i) she performs her duties well,
(ii) she is hospitable to relations and attendants
(iii) she is faithful,
(iv) she protects what he brings,
(v) she is skilled and industrious in discharging her duties.
"In these five ways does the wife show her compassion to her husband who ministers to her as the West. Thus is the West covered by him and made safe and secure."
May all be at peace.
John