Mr Caldbeck’s actions were one of several sexism scandals to rock Silicon Valley in recent months.
They include a damning report into the work culture inside ride-hailing firm Uber, and the resignation of venture capitalist Dave McClure, who admitted “inexcusable behaviour” towards “multiple women”.
No allegations have been made against Jonathan Teo, who said he had offered to step down in order to “quell a news cycle”.
He blamed leaks to a “corrupted” media about investors feeling nervous about his firm and claimed his resignation offer had not yet been accepted.
Mr Teo also said he was “angry that women had felt hurt”, but described a suggestion by one of the firm’s portfolio companies that the next partner should be a woman as “moronic”.
“We must choose the best person, male or female,” he wrote in the email, which the BBC has confirmed to be genuine.
“Talent is universal if we only choose to recognize it. Anything else is again grandstanding for a personal agenda.”
Mr Teo also added that reports suggesting investors were trying to buy back shares were untrue, and said that it was “dishonourable” for an entrepreneur to back away “at the first sign of trouble”.
Only one firm has so far announced its intention to pull away from Binary Capital.
Silicon Valley is full of “entitled human beings”, Mr Teo continued.
“As for the people here that whine that they aren’t taken care of, who have not to worry about their lives being taken from them or their basic needs met, who owes them more than the voice they already have access to?” he wrote.