No one is
forcing you to spay your puppy. It sounds like there are several things going on in the situation that you are describing in your post.
1. She is a puppy around 4-6 months old and you had a vet visit because she had a loose puppy tooth. While there the vet explained to you that small dogs like Yorkies have a tendency to retain their puppy teeth. This common issue needs to be addressed very soon for proper oral hygiene issues and the way this is done it under anesthesia which can be expensive. But it's usually a routine part of spay/neutering a puppy and included FREE or very close to free. Anesthesia cost is a large part many surgical procedures for most pets and it's just economical to to them together.
2. It sounds to me like you could possibly have some type of puppy insurance that reduces the price of the procedure. If I'm correct, this is why your vet is highly encouraging you to do this now since it's covered by your pet insurance. They are not forcing you
but trying to explain to you the benefits of your coverage which benefits both you and your puppy. Most puppies are spayed (btw females are spayed & males are neutered) around the 6 month or so range so I am guessing that your policy covers this only up until a certain again then it becomes an out of pocket expense.
3. You want to use her to breed some time in the future. Here's what I can offer you regarding breeding your little one. I'm guessing that you have no experience as a breeder since you didn't realize that she was losing a puppy tooth and needed vetting assistance. What will you do when it's time for her to whelp a litter of puppies? What if she has complications and needs a c-section or a puppy gets stuck in the birth channel? What is a puppy is breech or not breathing? What if she were to die (yes that has happened and there are posts right here on YT) during birth?
4. Do you have breeding rights for your puppy and where was she purchased?
5. Birds and the bees here.....you need a male to mate with. Where are you planning on finding a male to mate with your little girl? Usually, there is either a cost or you need to agree to pick of the litter to the owner of the male.
6. There are risks to not spaying your female puppy.
a.
Pyometra Pyometra is defined as an infection in the uterus. Pyometra is considered a serious and life threatening condition that must be treated quickly and aggressively. Pyometra is a secondary infection that occurs as a result of hormonal changes in the female's reproductive tract. During estrus ("heat"), white blood cells, which normally protect against infection, are inhibited from entering the uterus. This allows sperm to safely enter the female's reproductive tract without being damaged or destroyed by these immune system cells. Following estrus ("heat") in the dog, progesterone hormone levels remain elevated up to two months and cause thickening of the lining of the uterus in preparation for pregnancy and fetal development. If pregnancy does not occur for several consecutive estrus cycles, the uterine lining continues to increase in thickness until cysts often form within the tissues (a condition called Cystic Endometrial Hyperplasia). The thickened, cystic lining secretes fluids that create an ideal environment for bacteria to grow in. Additionally, high progesterone levels inhibit the ability of the muscles in the wall of the uterus to contract and expel accumulated fluids or bacteria. The combination of these factors often leads to infection.
Canine Mammary Tumors
Mammary tumors in dogs are most frequent in intact bitches; they are extremely rare in male dogs. Ovariectomy before the first estrus
reduces the risk of mammary neoplasia to 0.5% of the risk in intact bitches; ovariectomy after 1 estrus reduces the risk to 8% of that in intact bitches. Bitches neutered after maturity have generally been considered to have the same risk as intact bitches. However, questions remain regarding the impact of ovariohysterectomy at the time of tumor excision. Questions also remain about the timing of such surgery relative to survival. In one study, dogs spayed <2 yr prior to tumor excision lived 45% longer than either intact dogs or those spayed >2 yr prior to tumor excision.
* take note of the BOLD statement above
Let me add this as a little food for thought.
If you were to decide to breed your puppy in the future after even one litter of puppies and you added up the costs involved in breeding (vetting, tail docking, dew claws, puppy shots for the litter, and even the possibility of an emergency c-section which could easily be over $1500 and then eventual spaying her) is it really worth the cost or possible dangers to her health both during a whelping or her future health? Wouldn't it just be cheaper and less worrisome to spay her now under your insurance and buy another puppy in the future? 
I hope this gives you a little better understanding of why your vet has been discussing and not becoming more insistent on the idea of spaying her now while she is young, needs puppy teeth remove(they can't be left or there will be decay) and covered by your insurance. Makes total sense to me.