Because she wrote it for a computer invented by her husband Charles
Babbage,
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Lady Ada was not married to Babbage - she was married to the Count, and
that "Counts Babbage out" :-)
She was, as you referenced, the first programmer, as she wrote about how to
make his (Babbage) Analytical Engine solve different problems. While he
built and demonstrated the Differential Engine, the Analytical Engine was
never completed.