What can it mean when a man is forgetful and nervous around a girl?

Stress effect: A person performs at their best when: physically well, well rested, well nourished (not hungry) and in a familiar or non stressful setting. If a male has these symptoms around a girl, it is likely evidence of stress and normal. Improvement can come with making the situation more common or less stressful. If it is a phobic response, therapy may be a way to defeat the stress.

Performance anxiety: Certainly shallow breathing can cause undue anxiety - not warranted by the situation - and alter attention/short-term memory temporarily. When one wants to do very well they unwittingly shut down breathing - breathe less often, and more shallow. Heightened somatic awareness and anxiety consistent cognitions can predominate eventuating in catastrophic images, i.e., failure, ridicule, or shame.