Is there a reason not to battle every time?

On weekends in Fire Emblem 3 Houses, you're given 4 options:

• Explore Monastery
• Hold Seminar
• Battle
• Rest

It seems like exploring the Monastery is good for engaging your students so they'll be more inclined to learn, but why not just throw them straight into the field and let them increase their skills there (while also gaining levels--something they can't do in the classroom)?

Holding a Seminar is also good for increasing your students' skills, but again, doesn't battle do the same thing but better?

And lastly, Rest will increase your students' motivation so they can learn more. But--once again--why rely on classroom learning when they can learn the same things (and more) out in the field?

Am I missing something? Is there a good reason not to always select Battle to train the students?

Yes, there is.

There are a couple of things that are only available if you explore the Monastery, but the most important reason for not battling every time is: efficiency.

When you play on Hard difficulty or higher, each battle consumes time. This means you are limited to only 1 battle at a time until you raise your Teacher Skill to C+ or higher. The fastest way to do that, is to explore the Monastery as often as possible.

Teacher Skill is also important for unlocking various things, such as Master Classes or additional forging blueprints at the Blacksmith's. Higher Teacher Skill also means more timeslots for use during Instruction or Exploration, further improving your efficiency.

Even if you play on Normal difficulty, grinding from level 1 to level 40 is not advised. When you Certify for a higher-tier class, your level does not reset. Since higher-tier classes improve your growth rate, you'll be missing out on a lot of growth by grinding levels early.

If you want to maximize growth, it is therefore better to only grind up to levels 5, 10, 20, and 30, so you can Certify for the next best class. To do so, you'll need high enough Skills. Training skills in battle without increasing your level is pretty much impossible.

This is why Seminars and Motivation are important, even if you can improve skills in battle.

Motivation is also the only way to Instruct a student directly, which in turn is the only way to develop Budding Talents. Once developed, a Budding Talent becomes a Strength (Skill develops more quickly), even if it used to be a Weakness (Skill develops more slowly).

The following lists are based on a playthrough up to 9/30. Playing further may reveal additional reasons to not battle every Sunday.

Explore Monastery

• You can get quests which will increase your Renown and award you with free items.

• It's the only place where you can spend Renown for additional benefits, such as increasing Class Mastery by 2 instead of 1 every time you engage an enemy.

• You can recruit students from other houses, as well as some non-students.

• Aside from answering questions on Mondays, it is the only place where you can improve your Teacher Skill.

• Harvesting crops may yield items that can permanently increase your stats. Higher Teacher Skill lets you plant more seeds at a time to improve your odds.

• The Eastern and Southern Merchants (unlocked through quest) are only accessible from within the Monastery. Among others, the Eastern Merchant sells materials necessary for weapon repairs and forging.

• Asking other teachers for instruction is the only way to develop your own Budding Talent (Faith). Each teacher can only improve 1 skill, and only once a day.

Hold Seminar

• It's the only way to improve student Skills on Sunday, other than Faith (Choir Practice). Improves 2 Skills at a time for up to 6 people (5 students + Byleth) and improves their Motivation.

Rest

• Recovers durability for the Sword of Creation for free, whereas the Blacksmith requires 2 Umbral Steel and 2500G.