How to Fix: Music Won't Sync to iPhone
Double check if the songs on your iTunes library have same folder location as before. Sometimes iTunes does not indicate which songs it cannot find until you select them. Songs in your library that iTunes can't locate, won't be synced to your iPhone, iPad or iPod.
When syncing music to iPhone/iPad/iPod with iTunes, go to the Music tab - is "Entire music library" selected? If not, go to Music (in your iTunes library), click on the check mark next to the "Name" column header (to sort by checked music) and scroll to the bottom, or any unchecked music won't sync.

Fix Music Won't Sync to iPhone with an iTunes Alternative
Apart from syncing devices, iTunes is also overhauled with iTunes Store, Media Player functions. So it's no wonder iTunes get everything well-organized. However, when syncing media files (like Music, Apps, iBooks, etc.) with iTunes, you may meet many kinds of iTunes problems, like:
iTunes synced songs are greyed out, and can't be played
iTunes reminds you "Are you sure you want to remove existing music, movies, TV shows, books and tones from this iPhone/iPad/iPod and sync with this iTunes library?"
Or just like the problem mentioned in this guide, some music or songs won't sync to iPhone/iPad/iPod
No matter which situation you stuck on, you can try to fix it by using some iTunes alternative, like AnyTrans, which can be regarded as the best iTunes alternative, which allows you to transfer & manage music on iPhone iPad iPod with ease. And fitted with some fantastic features, like:
Sync music to iPhone/iPad/iPod without replacing any existed data.
Get songs from iPhone back to computer or iTunes including non-iTunes purchased music.
Copy music from iPhone to iPhone, to iPod and to iPad directly.
Also manages photos, videos, ringtones, audiobooks, voice memos, contacts, notes, messages and more on iPhone/iPad/iPod touch.

Supports all the models of iPhone, iPad and iPod, including iPhone 4/4s/5/5s/5c/6/6s/SE and the latest iPhone 7 and iPhone 7 Plus, etc. No matter what device you are working with, you can use AnyTrans to fix this "music won't sync to iDevice" problem.
Step 1: Get AnyTrans installed on computer, run it and then connect your iPhone or iPad to computer.
Step 2: On homepage of AnyTrans, click iTunes Library tab > Select Music tab > Select the songs that can't sync to iPhone/iPad/iPod > Click To iDevice button to transfer music from iTunes Library to iPhone/iPad/iPod again.