Given the context of the original statement you want to paraphrase, you should not use either term.
The specific language you want to paraphrase is
I think it can be due to our upbringing. We want what we want when we want it.
You've proposed
today’s teens are much too pampered and as a result, lazy.
You've got a great start with reformulating the sentences so that you can replace "due to" with "as a result". You have also (like the narrator of the original piece) paraphrased the second half of the quote as "lazy", which works fine.
Your sticking point is how to paraphrase "our upbringing". You have proposed either "pampering" or "spoon-feeding" as replacements, but neither is really appropriate here.
When paraphrasing someone else's words, it's very important not to mis-characterize the original meaning. In this case, the original speaker talked about "our upbringing" and its results ("lazy" and "want what we want when we want it"). But she did not specify what aspect of rearing caused these result.
You have inferred that these lazy young people's parents were "pampering" or "spoon-feeding" them, and that has caused them to behave this way. But perhaps, instead, Ms. Benoit meant that she and her peers had been particularly deprived for most of their childhoods, and now that they don't have to work as hard they don't want to. That scenario might not seem as likely to you (it doesn't to me, either) but the original statement leaves open the possibility.
So, what should you use?
Look for a neutral synonym for "upbringing", or just use "upbringing", and then leave the specific deficits of this to the imagination of the reader (like the original speaker did). You may need to rearrange your sentence slightly to make this work. I would suggest something like
today's teens are lazy as a result of their upbringing.
or
as a result of the way today's teens were raised, they are lazy.
or, to stick as close as possible to your original structure,
today's teens were raised to be entitled and as a result, lazy.
Note that in that last example, I have substituted the adjective entitled for the statement that teens "want what [they] want when [they] want it", as suggested by Rhythmatic. That works, since you actually do have two descriptions of the young people in the original, and you were previously using the single word "lazy" to stand in for both. What we don't have is a description of the teens' parents' parenting style.
Best Answer
To me, leap, bound and spring have slightly different emphasis compared with the more neutral noun jump. At least to my ears:
a leap emphasises the distance, or gymnastic ability of the jump.
a bound emphasises the energy or perhaps the enthusiasm of the jump.
a spring emphasises the speed or the unexpectedness of the jump.
So for example, I might use them in the following sentences:
In the context of your sentence, where the emphasis is on the nimbleness and perhaps distance of the jump, I would therefore choose leap, although I would avoid mixing leap with sprung, instead preferring a more neutral noun to go with the verb leapt or a more neutral verb to go with the noun leap: