Providence Equity Partners Puns

Got a question here, I’ve got a startup that sells climbing gear. I have a business connection that allowed us to acquire the inventory for a fraction of the wholesale price (worth about 250k retail, paid 40k). Recently, my business partner has told me that I need to sell back half my equity (for nothing) so he can pitch the business to investors by giving them the equity I sold back. Is this a common thing? I figured that if we get investors onboard we can transfer our own equity rather then having it floating around in the business, or is it there a reason to pitch the business with non-vested equity?

I recently bought a house and my fiance is saying that he wants equity because he is paying half the mortgage. Our original plan was to add him to the title once he'd payed half the cost of the downpayment because he was not able to help with any of the purchase costs. However recently, he said he won't make any more mortgage payments until we have in writing that it's counting towards equity.

We split all the bills equally. I do most of the cooking and cleaning, he's doing most of the repairs/maintenance that won't require permits.

We approach finances very differently and have always had separate bank accounts. I'm hesitant about the equity thing because on the chance things don't work out - 1. I really don't want to lose the house 2. I don't know if I'd have the liquid cash to buy him out and the house has a 60k foundation issue I need to save up for to fix

So I'm not sure if I should just pay the full mortgage in the meantime or if he already may have equity by default because he's been paying half the mortgage for 6 months.

Any advise would be much appreciated!

Edit: Thank you everyone for the responses. I really appreciate it and it's given me a lot to think about. I think I'm going to propose this to him:

Mortgage payments he's paid to date/(total mortgage amount + downpayment & closing costs + foundation repair cost + loan interest to date)/2 to get the percent equity.

And then equity x (1/2 current home value on Zillow)

Meri is so incredibly annoying. She wants a loan from everyone’s pooled money but she doesn’t want everyone to be partners (they even suggested silent partners) on the business. I don’t love Robyn, or Kody at all but why in the name of god would they have all their names on all their businesses AND give her money for this one and get NOTHING out of it? She physically jumped back and shook her head when they asked if they’d share equity the first time and then when they bring it up she pulls her “my walls are up” bullshit which I can’t stand and keeps saying “I didn’t say that you weren’t!!” When she absolutely did. And then when she says “well don’t expect to see me at family functions because I need to raise the money” which was SO passive aggressive and snarky. I just genuinely can’t stand her, I’m sorry. Obviously Kotex and Sobyn are the worst but so is Meri, thanks for coming to my Ted talk 😂.

...but not 100% sure I want to be a partner. Which is crazy for me because that's all I've been working towards/wanting since I started in public accounting. I mean this is the time when PA starts to pay off right? Just feeling disenchanted with my firm and the PA lifestyle in general. It just seems like there is so much more drama/politics between partners and they totally lose sight of the day to day concerns of the people who make the firm function. The last 2 or so years I've just been burnt out (I know, unheard of in out profession /s). A couple of my close coworkers who I swore I would be partners with, left this year and it just has me wondering if getting partnership is really what I want?

If not, I have absolutely no idea what is next in my career and feel super pissed I got used by the system.