Engineered hardwood has a plywood base with a thin veneer of real wood on top, which actually makes it more stable in moisture-prone environments than solid hardwood. Your contractor's right about that part - solid wood expands and contracts with humidity swings, which is rough for kitchens and bathrooms. Engineered holds up better to those conditions because the cross-grain plywood construction resists warping. That said, it's not indestructible. The veneer can still scratch, dent, and wear down over time, and once it does, you can't sand it back to life the way you can with solid wood.
The durability question really depends on the quality of the engineered product. A cheap engineered floor with a thin veneer might need replacing in 10-15 years if it gets heavy use. A solid engineered floor with a thicker veneer (like 2-3mm) can easily last 20+ years. Since you're staying put for 15 years, a mid-to-high quality engineered product should absolutely get you there without issues. You probably won't need replacing at that timeframe if you're not doing crazy things to it.
Price-wise, engineered is typically cheaper upfront, sometimes by 30-40% or so depending on what you compare. For a kitchen and bathroom specifically, that moisture resistance is genuinely valuable - solid wood in those rooms is asking for trouble. I'd say go for it, but make sure your contractor's sourcing decent quality stuff, not bargain-basement material. Ask what the veneer thickness is and what the warranty covers. That matters way more than just "engineered vs. solid.