You've got several huge red flags right here:
- emails with a giant font
- HR responding to applications after 3 months
- HR calling you without leaving a message
- HR apparently blaming you for their failure to communicate or follow professional norms
The only "mistake" you made is not answering your phone because you didn't recognize the number. Since you're presumably applying for jobs, you generally want to answer these calls. Of course, if you aren't actively looking and your last contact was 3 months ago then even this isn't a problem.
How to respond?
Now, just because that HR staffer and possibly their entire HR department is incompetent, that doesn't necessarily mean that you should extrapolate their behaviour to the rest of the company and your potential colleagues (See: Does bad HR mean a bad company?). But it's not a good sign and if you choose to continue the process be very alert for any other red flags from management or potential colleagues. Also consider that a consistently unprofessional hiring process is likely to mean that the people they hire (i.e. your future colleagues) aren't great. High performers don't put up with this kind of treatment because they have plenty of options.
If you don't mind putting up with this so you can get an interview with the actual hiring manager, I'd simply email back with a variation of the following.
Thank you for reaching out to me. [Due to a high volume of commercial
calls] I generally do not answer my phone when called by unknown
numbers. [As I last reached out to you three months ago I wasn't
expecting to receive calls from new numbers.] I assumed that someone
was calling the wrong number as you didn't leave a message on my
voicemail. I'm still interested in the position and if you'd like we
can set up a time for a phone call so we don't miss each other.
[Close and formalities]
Your tone should be apologetic, not because you did anything wrong, but because this person has already shown you a lot of irrational behaviour and your goal is to get in touch with someone sane. Skip or replace the bracketed sections if they don't fit.
If you are no longer interested in applying for their current position, just replace the last line with some variation of:
Since I originally applied for the position of X, I've [accepted a new position at][decided to remain with my current employer][relocated][been promoted] so I would like to withdraw my application from consideration. [If you have any openings in the future I would appreciate being considered.]